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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 23520.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23520.bv1 | 23520v4 | \([0, 1, 0, -3213240, -2217954600]\) | \(60910917333827912/3255076125\) | \(196073702927424000\) | \([2]\) | \(442368\) | \(2.3855\) | |
| 23520.bv2 | 23520v3 | \([0, 1, 0, -1038865, 379651775]\) | \(257307998572864/19456203375\) | \(9375755759064576000\) | \([2]\) | \(442368\) | \(2.3855\) | |
| 23520.bv3 | 23520v1 | \([0, 1, 0, -211990, -30643600]\) | \(139927692143296/27348890625\) | \(205924456521000000\) | \([2, 2]\) | \(221184\) | \(2.0389\) | \(\Gamma_0(N)\)-optimal |
| 23520.bv4 | 23520v2 | \([0, 1, 0, 436280, -180782932]\) | \(152461584507448/322998046875\) | \(-19456203375000000000\) | \([2]\) | \(442368\) | \(2.3855\) |
Rank
sage: E.rank()
The elliptic curves in class 23520.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 23520.bv do not have complex multiplication.Modular form 23520.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
