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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 38640.cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.cv1 | 38640cv1 | \([0, 1, 0, -3920, -91500]\) | \(1626794704081/83462400\) | \(341861990400\) | \([2]\) | \(73728\) | \(0.97102\) | \(\Gamma_0(N)\)-optimal |
| 38640.cv2 | 38640cv2 | \([0, 1, 0, 2480, -355180]\) | \(411664745519/13605414480\) | \(-55727777710080\) | \([2]\) | \(147456\) | \(1.3176\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.cv have rank \(0\).
Complex multiplication
The elliptic curves in class 38640.cv do not have complex multiplication.Modular form 38640.2.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 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.
