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SageMath
E = EllipticCurve("gr1")
E.isogeny_class()
Elliptic curves in class 303450.gr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 303450.gr1 | 303450gr4 | \([1, 0, 0, -2113836463, 35312378159417]\) | \(2769646315294225853641/174474906948464640\) | \(65803126644330385813440000000\) | \([2]\) | \(382205952\) | \(4.2808\) | |
| 303450.gr2 | 303450gr2 | \([1, 0, 0, -2080782088, 36533051843792]\) | \(2641739317048851306841/764694000\) | \(288403971701343750000\) | \([2]\) | \(127401984\) | \(3.7314\) | |
| 303450.gr3 | 303450gr1 | \([1, 0, 0, -130032088, 570975593792]\) | \(-644706081631626841/347004000000\) | \(-130872390519937500000000\) | \([2]\) | \(63700992\) | \(3.3849\) | \(\Gamma_0(N)\)-optimal |
| 303450.gr4 | 303450gr3 | \([1, 0, 0, 105683537, 2319213359417]\) | \(346124368852751159/6361262220902400\) | \(-2399146965376951910400000000\) | \([2]\) | \(191102976\) | \(3.9342\) |
Rank
sage: E.rank()
The elliptic curves in class 303450.gr have rank \(0\).
Complex multiplication
The elliptic curves in class 303450.gr do not have complex multiplication.Modular form 303450.2.a.gr
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
