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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 155848.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 155848.v1 | 155848n2 | \([0, -1, 0, -59088, -5508292]\) | \(12576878500/1127\) | \(2044466428928\) | \([2]\) | \(409600\) | \(1.4022\) | |
| 155848.v2 | 155848n1 | \([0, -1, 0, -3428, -98140]\) | \(-9826000/3703\) | \(-1679383138048\) | \([2]\) | \(204800\) | \(1.0556\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 155848.v have rank \(1\).
Complex multiplication
The elliptic curves in class 155848.v do not have complex multiplication.Modular form 155848.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
