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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 308550.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 308550.h1 | 308550h7 | \([1, 1, 0, -608740359625, 182808192998717125]\) | \(901247067798311192691198986281/552431869440\) | \(15291668047765560000000\) | \([2]\) | \(1911029760\) | \(4.9645\) | |
| 308550.h2 | 308550h8 | \([1, 1, 0, -38301831625, 2816047326653125]\) | \(224494757451893010998773801/6152490825146276160000\) | \(170304887479483783441965000000000\) | \([2]\) | \(1911029760\) | \(4.9645\) | |
| 308550.h3 | 308550h6 | \([1, 1, 0, -38046279625, 2856364999037125]\) | \(220031146443748723000125481/172266701724057600\) | \(4768452662077706342400000000\) | \([2, 2]\) | \(955514880\) | \(4.6179\) | |
| 308550.h4 | 308550h4 | \([1, 1, 0, -7516845250, 250655549321500]\) | \(1696892787277117093383481/1440538624914939000\) | \(39875031982702097652796875000\) | \([2]\) | \(637009920\) | \(4.4151\) | |
| 308550.h5 | 308550h5 | \([1, 1, 0, -4922847250, -131526938112500]\) | \(476646772170172569823801/5862293314453125000\) | \(162272034475717071533203125000\) | \([2]\) | \(637009920\) | \(4.4151\) | |
| 308550.h6 | 308550h3 | \([1, 1, 0, -2361927625, 45258801533125]\) | \(-52643812360427830814761/1504091705903677440\) | \(-41634221978162886082560000000\) | \([2]\) | \(477757440\) | \(4.2713\) | |
| 308550.h7 | 308550h2 | \([1, 1, 0, -574470250, 2042158196500]\) | \(757443433548897303481/373234243041000000\) | \(10331362950561828140625000000\) | \([2, 2]\) | \(318504960\) | \(4.0686\) | |
| 308550.h8 | 308550h1 | \([1, 1, 0, 131201750, 244811612500]\) | \(9023321954633914439/6156756739584000\) | \(-170422970723971416000000000\) | \([2]\) | \(159252480\) | \(3.7220\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 308550.h have rank \(0\).
Complex multiplication
The elliptic curves in class 308550.h do not have complex multiplication.Modular form 308550.2.a.h
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 3 & 12 & 4 & 6 & 12 \\ 4 & 1 & 2 & 12 & 3 & 4 & 6 & 12 \\ 2 & 2 & 1 & 6 & 6 & 2 & 3 & 6 \\ 3 & 12 & 6 & 1 & 4 & 12 & 2 & 4 \\ 12 & 3 & 6 & 4 & 1 & 12 & 2 & 4 \\ 4 & 4 & 2 & 12 & 12 & 1 & 6 & 3 \\ 6 & 6 & 3 & 2 & 2 & 6 & 1 & 2 \\ 12 & 12 & 6 & 4 & 4 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
