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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 139200.cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139200.cv1 | 139200ej2 | \([0, -1, 0, -10417633, 12983339137]\) | \(-30526075007211889/103499257854\) | \(-423932960169984000000\) | \([]\) | \(5268480\) | \(2.8221\) | |
139200.cv2 | 139200ej1 | \([0, -1, 0, -1633, -8772863]\) | \(-117649/8118144\) | \(-33251917824000000\) | \([]\) | \(752640\) | \(1.8491\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 139200.cv have rank \(0\).
Complex multiplication
The elliptic curves in class 139200.cv do not have complex multiplication.Modular form 139200.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.