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SageMath
E = EllipticCurve("fv1")
E.isogeny_class()
Elliptic curves in class 119952fv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
119952.c1 | 119952fv1 | \([0, 0, 0, -17787, -579670]\) | \(1771561/612\) | \(214994395348992\) | \([2]\) | \(552960\) | \(1.4519\) | \(\Gamma_0(N)\)-optimal |
119952.c2 | 119952fv2 | \([0, 0, 0, 52773, -4037110]\) | \(46268279/46818\) | \(-16447071244197888\) | \([2]\) | \(1105920\) | \(1.7985\) |
Rank
sage: E.rank()
The elliptic curves in class 119952fv have rank \(0\).
Complex multiplication
The elliptic curves in class 119952fv do not have complex multiplication.Modular form 119952.2.a.fv
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.