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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 22848.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22848.bv1 | 22848bh4 | \([0, 1, 0, -5089, 138047]\) | \(444893916104/9639\) | \(315850752\) | \([2]\) | \(14336\) | \(0.74729\) | |
| 22848.bv2 | 22848bh2 | \([0, 1, 0, -329, 1911]\) | \(964430272/127449\) | \(522031104\) | \([2, 2]\) | \(7168\) | \(0.40071\) | |
| 22848.bv3 | 22848bh1 | \([0, 1, 0, -84, -294]\) | \(1036433728/122451\) | \(7836864\) | \([2]\) | \(3584\) | \(0.054141\) | \(\Gamma_0(N)\)-optimal |
| 22848.bv4 | 22848bh3 | \([0, 1, 0, 511, 10815]\) | \(449455096/1753941\) | \(-57473138688\) | \([2]\) | \(14336\) | \(0.74729\) |
Rank
sage: E.rank()
The elliptic curves in class 22848.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 22848.bv do not have complex multiplication.Modular form 22848.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
