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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 397800cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
397800.cv2 | 397800cv1 | \([0, 0, 0, 2850, -14375]\) | \(14047232/8619\) | \(-1570812750000\) | \([2]\) | \(524288\) | \(1.0294\) | \(\Gamma_0(N)\)-optimal |
397800.cv1 | 397800cv2 | \([0, 0, 0, -11775, -116750]\) | \(61918288/33813\) | \(98598708000000\) | \([2]\) | \(1048576\) | \(1.3760\) |
Rank
sage: E.rank()
The elliptic curves in class 397800cv have rank \(1\).
Complex multiplication
The elliptic curves in class 397800cv do not have complex multiplication.Modular form 397800.2.a.cv
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.