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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 37570d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37570.a1 | 37570d1 | \([1, 0, 1, -3619, 85086]\) | \(-62736640489/1406080\) | \(-117437207680\) | \([3]\) | \(51408\) | \(0.91248\) | \(\Gamma_0(N)\)-optimal |
| 37570.a2 | 37570d2 | \([1, 0, 1, 15166, 378132]\) | \(4619365699751/3407872000\) | \(-284628877312000\) | \([]\) | \(154224\) | \(1.4618\) |
Rank
sage: E.rank()
The elliptic curves in class 37570d have rank \(1\).
Complex multiplication
The elliptic curves in class 37570d do not have complex multiplication.Modular form 37570.2.a.d
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.
