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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 11970.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11970.v1 | 11970l4 | \([1, -1, 0, -364974, -84747052]\) | \(273161111316733107/108726499840\) | \(2140063696350720\) | \([2]\) | \(186624\) | \(1.9056\) | |
| 11970.v2 | 11970l3 | \([1, -1, 0, -19374, -1733932]\) | \(-40860428336307/42709811200\) | \(-840657213849600\) | \([2]\) | \(93312\) | \(1.5590\) | |
| 11970.v3 | 11970l2 | \([1, -1, 0, -12999, 429093]\) | \(8997224809453803/2305248169000\) | \(62241700563000\) | \([6]\) | \(62208\) | \(1.3563\) | |
| 11970.v4 | 11970l1 | \([1, -1, 0, 2001, 42093]\) | \(32807952226197/48013000000\) | \(-1296351000000\) | \([6]\) | \(31104\) | \(1.0097\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11970.v have rank \(0\).
Complex multiplication
The elliptic curves in class 11970.v do not have complex multiplication.Modular form 11970.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
