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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 185150.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185150.a1 | 185150bn2 | \([1, 0, 1, -2089826, 2681098548]\) | \(-17455277065/43606528\) | \(-2521613726048200000000\) | \([]\) | \(13685760\) | \(2.7945\) | |
185150.a2 | 185150bn1 | \([1, 0, 1, 224549, -82265202]\) | \(21653735/63112\) | \(-3649547276003125000\) | \([]\) | \(4561920\) | \(2.2452\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 185150.a have rank \(1\).
Complex multiplication
The elliptic curves in class 185150.a do not have complex multiplication.Modular form 185150.2.a.a
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 LMFDB 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 LMFDB labels.