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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 453152e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
453152.e2 | 453152e1 | \([0, 1, 0, 23602, 1006480]\) | \(8000/7\) | \(-1272212863165888\) | \([2]\) | \(1966080\) | \(1.5858\) | \(\Gamma_0(N)\)-optimal* |
453152.e1 | 453152e2 | \([0, 1, 0, -118008, 8823352]\) | \(125000/49\) | \(71243920337289728\) | \([2]\) | \(3932160\) | \(1.9324\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 453152e have rank \(2\).
Complex multiplication
The elliptic curves in class 453152e do not have complex multiplication.Modular form 453152.2.a.e
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.