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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 8880.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8880.v1 | 8880t2 | \([0, 1, 0, -338336, 75614964]\) | \(1045706191321645729/323352324000\) | \(1324451119104000\) | \([2]\) | \(57600\) | \(1.8781\) | |
8880.v2 | 8880t1 | \([0, 1, 0, -18336, 1502964]\) | \(-166456688365729/143856000000\) | \(-589234176000000\) | \([2]\) | \(28800\) | \(1.5316\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8880.v have rank \(1\).
Complex multiplication
The elliptic curves in class 8880.v do not have complex multiplication.Modular form 8880.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.