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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 213444v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
213444.u2 | 213444v1 | \([0, 0, 0, -1565256, 718126409]\) | \(131072/7\) | \(22649987021533380432\) | \([2]\) | \(5474304\) | \(2.4704\) | \(\Gamma_0(N)\)-optimal |
213444.u1 | 213444v2 | \([0, 0, 0, -4500111, -2762024650]\) | \(194672/49\) | \(2536798546411738608384\) | \([2]\) | \(10948608\) | \(2.8170\) |
Rank
sage: E.rank()
The elliptic curves in class 213444v have rank \(0\).
Complex multiplication
The elliptic curves in class 213444v do not have complex multiplication.Modular form 213444.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.