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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 289296v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
289296.v1 | 289296v1 | \([0, 0, 0, -399, -3206]\) | \(-768208/41\) | \(-374927616\) | \([]\) | \(138240\) | \(0.40411\) | \(\Gamma_0(N)\)-optimal |
289296.v2 | 289296v2 | \([0, 0, 0, 2121, -6734]\) | \(115393712/68921\) | \(-630253322496\) | \([]\) | \(414720\) | \(0.95342\) |
Rank
sage: E.rank()
The elliptic curves in class 289296v have rank \(0\).
Complex multiplication
The elliptic curves in class 289296v do not have complex multiplication.Modular form 289296.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.