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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 7488.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7488.bv1 | 7488z2 | \([0, 0, 0, -104484, 12995552]\) | \(42246001231552/14414517\) | \(43041517129728\) | \([2]\) | \(24576\) | \(1.5877\) | |
| 7488.bv2 | 7488z1 | \([0, 0, 0, -5619, 261740]\) | \(-420526439488/390971529\) | \(-18241167657024\) | \([2]\) | \(12288\) | \(1.2411\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7488.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 7488.bv do not have complex multiplication.Modular form 7488.2.a.bv
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.
