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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 327990.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 327990.z1 | 327990z1 | \([1, 1, 1, -53768091, 171055701513]\) | \(-40861808665609/6406452000\) | \(-2695240696190539296852000\) | \([]\) | \(65772000\) | \(3.4163\) | \(\Gamma_0(N)\)-optimal |
| 327990.z2 | 327990z2 | \([1, 1, 1, 359991294, -616907671281]\) | \(12263649421047431/7488000000000\) | \(-3150255762951905088000000000\) | \([]\) | \(197316000\) | \(3.9656\) |
Rank
sage: E.rank()
The elliptic curves in class 327990.z have rank \(1\).
Complex multiplication
The elliptic curves in class 327990.z do not have complex multiplication.Modular form 327990.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
