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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 5880f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5880.n1 | 5880f1 | \([0, -1, 0, -2515, -35888]\) | \(2725888/675\) | \(435818955600\) | \([2]\) | \(5376\) | \(0.94371\) | \(\Gamma_0(N)\)-optimal |
5880.n2 | 5880f2 | \([0, -1, 0, 6060, -234828]\) | \(2382032/3645\) | \(-37654757763840\) | \([2]\) | \(10752\) | \(1.2903\) |
Rank
sage: E.rank()
The elliptic curves in class 5880f have rank \(1\).
Complex multiplication
The elliptic curves in class 5880f do not have complex multiplication.Modular form 5880.2.a.f
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.