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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 133518.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 133518.bv1 | 133518o3 | \([1, 1, 1, -11631389, 15263622281]\) | \(7209828390823479793/49509306\) | \(1195034289717114\) | \([2]\) | \(3932160\) | \(2.4928\) | |
| 133518.bv2 | 133518o4 | \([1, 1, 1, -1013529, 32982417]\) | \(4770223741048753/2740574865798\) | \(66150814922864965062\) | \([2]\) | \(3932160\) | \(2.4928\) | |
| 133518.bv3 | 133518o2 | \([1, 1, 1, -727419, 237951621]\) | \(1763535241378513/4612311396\) | \(111329984570436324\) | \([2, 2]\) | \(1966080\) | \(2.1463\) | |
| 133518.bv4 | 133518o1 | \([1, 1, 1, -28039, 6596717]\) | \(-100999381393/723148272\) | \(-17455041312630768\) | \([2]\) | \(983040\) | \(1.7997\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 133518.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 133518.bv do not have complex multiplication.Modular form 133518.2.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.
