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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 117670.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117670.m1 | 117670m4 | \([1, -1, 1, -449983, -116064619]\) | \(2121328796049/120050\) | \(570250014132050\) | \([2]\) | \(1126400\) | \(1.8958\) | |
| 117670.m2 | 117670m3 | \([1, -1, 1, -147403, 20392237]\) | \(74565301329/5468750\) | \(25977132567968750\) | \([2]\) | \(1126400\) | \(1.8958\) | |
| 117670.m3 | 117670m2 | \([1, -1, 1, -29733, -1588519]\) | \(611960049/122500\) | \(581887769522500\) | \([2, 2]\) | \(563200\) | \(1.5492\) | |
| 117670.m4 | 117670m1 | \([1, -1, 1, 3887, -149583]\) | \(1367631/2800\) | \(-13300291874800\) | \([2]\) | \(281600\) | \(1.2026\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 117670.m have rank \(1\).
Complex multiplication
The elliptic curves in class 117670.m do not have complex multiplication.Modular form 117670.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
