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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 13950m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13950.v3 | 13950m1 | \([1, -1, 0, -24417, 1311741]\) | \(141339344329/17141760\) | \(195255360000000\) | \([2]\) | \(55296\) | \(1.4726\) | \(\Gamma_0(N)\)-optimal |
| 13950.v2 | 13950m2 | \([1, -1, 0, -96417, -10136259]\) | \(8702409880009/1120910400\) | \(12767870025000000\) | \([2, 2]\) | \(110592\) | \(1.8192\) | |
| 13950.v1 | 13950m3 | \([1, -1, 0, -1491417, -700661259]\) | \(32208729120020809/658986840\) | \(7506271974375000\) | \([2]\) | \(221184\) | \(2.1658\) | |
| 13950.v4 | 13950m4 | \([1, -1, 0, 146583, -53147259]\) | \(30579142915511/124675335000\) | \(-1420129987734375000\) | \([2]\) | \(221184\) | \(2.1658\) |
Rank
sage: E.rank()
The elliptic curves in class 13950m have rank \(0\).
Complex multiplication
The elliptic curves in class 13950m do not have complex multiplication.Modular form 13950.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
