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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 10304y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10304.bb2 | 10304y1 | \([0, -1, 0, 2207, -188415]\) | \(4533086375/60669952\) | \(-15904263897088\) | \([2]\) | \(21504\) | \(1.2139\) | \(\Gamma_0(N)\)-optimal |
10304.bb1 | 10304y2 | \([0, -1, 0, -38753, -2736127]\) | \(24553362849625/1755162752\) | \(460105384460288\) | \([2]\) | \(43008\) | \(1.5605\) |
Rank
sage: E.rank()
The elliptic curves in class 10304y have rank \(1\).
Complex multiplication
The elliptic curves in class 10304y do not have complex multiplication.Modular form 10304.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.