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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 481338y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
481338.y1 | 481338y1 | \([1, -1, 0, -1419595557, -48728930112747]\) | \(-6614510824496145219145875/17618041962927377281024\) | \(-842708773022910860430400278528\) | \([]\) | \(559872000\) | \(4.4297\) | \(\Gamma_0(N)\)-optimal* |
481338.y2 | 481338y2 | \([1, -1, 0, 12379254123, 1102135303183877]\) | \(6016719201015220250419125/18530931219677304938224\) | \(-646166810860794229786969133170512\) | \([]\) | \(1679616000\) | \(4.9790\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 481338y have rank \(0\).
Complex multiplication
The elliptic curves in class 481338y do not have complex multiplication.Modular form 481338.2.a.y
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.