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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 135240.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
135240.v1 | 135240bc1 | \([0, -1, 0, -660, -1308]\) | \(362642992/198375\) | \(17418912000\) | \([2]\) | \(98304\) | \(0.65581\) | \(\Gamma_0(N)\)-optimal |
135240.v2 | 135240bc2 | \([0, -1, 0, 2560, -12900]\) | \(5280558692/3234375\) | \(-1136016000000\) | \([2]\) | \(196608\) | \(1.0024\) |
Rank
sage: E.rank()
The elliptic curves in class 135240.v have rank \(1\).
Complex multiplication
The elliptic curves in class 135240.v do not have complex multiplication.Modular form 135240.2.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.