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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 1520i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1520.b1 | 1520i1 | \([0, 1, 0, -921, -10346]\) | \(5405726654464/407253125\) | \(6516050000\) | \([2]\) | \(960\) | \(0.62837\) | \(\Gamma_0(N)\)-optimal |
1520.b2 | 1520i2 | \([0, 1, 0, 884, -44280]\) | \(298091207216/3525390625\) | \(-902500000000\) | \([2]\) | \(1920\) | \(0.97495\) |
Rank
sage: E.rank()
The elliptic curves in class 1520i have rank \(1\).
Complex multiplication
The elliptic curves in class 1520i do not have complex multiplication.Modular form 1520.2.a.i
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.