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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 14490.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.q1 | 14490q1 | \([1, -1, 0, -2205, -37499]\) | \(1626794704081/83462400\) | \(60844089600\) | \([2]\) | \(24576\) | \(0.82718\) | \(\Gamma_0(N)\)-optimal |
14490.q2 | 14490q2 | \([1, -1, 0, 1395, -150539]\) | \(411664745519/13605414480\) | \(-9918347155920\) | \([2]\) | \(49152\) | \(1.1738\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.q have rank \(1\).
Complex multiplication
The elliptic curves in class 14490.q do not have complex multiplication.Modular form 14490.2.a.q
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.