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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 37570p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37570.g2 | 37570p1 | \([1, 0, 0, -961058235, 9878475982225]\) | \(827813553991775477153/123566310400000000\) | \(14653466356905166668800000000\) | \([2]\) | \(25067520\) | \(4.1289\) | \(\Gamma_0(N)\)-optimal |
| 37570.g1 | 37570p2 | \([1, 0, 0, -14777200315, 691392842819217]\) | \(3009261308803109129809313/85820312500000000\) | \(10177248619683945312500000000\) | \([2]\) | \(50135040\) | \(4.4755\) |
Rank
sage: E.rank()
The elliptic curves in class 37570p have rank \(1\).
Complex multiplication
The elliptic curves in class 37570p do not have complex multiplication.Modular form 37570.2.a.p
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.
