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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 312312.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 312312.bv1 | 312312bv4 | \([0, 1, 0, -6427464, -6274161360]\) | \(2970658109581346/2139291\) | \(21147543659354112\) | \([2]\) | \(7864320\) | \(2.4444\) | |
| 312312.bv2 | 312312bv3 | \([0, 1, 0, -924824, 203011056]\) | \(8849350367426/3314597517\) | \(32765806850935302144\) | \([2]\) | \(7864320\) | \(2.4444\) | |
| 312312.bv3 | 312312bv2 | \([0, 1, 0, -404304, -96808464]\) | \(1478729816932/38900169\) | \(192270014290658304\) | \([2, 2]\) | \(3932160\) | \(2.0978\) | |
| 312312.bv4 | 312312bv1 | \([0, 1, 0, 4676, -4869760]\) | \(9148592/8301447\) | \(-10257791767711488\) | \([2]\) | \(1966080\) | \(1.7512\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 312312.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 312312.bv do not have complex multiplication.Modular form 312312.2.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.
