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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 3800d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3800.f2 | 3800d1 | \([0, -1, 0, -650883, -202065988]\) | \(-121981271658244096/115966796875\) | \(-28991699218750000\) | \([2]\) | \(53760\) | \(2.0807\) | \(\Gamma_0(N)\)-optimal |
| 3800.f1 | 3800d2 | \([0, -1, 0, -10416508, -12936440988]\) | \(31248575021659890256/28203125\) | \(112812500000000\) | \([2]\) | \(107520\) | \(2.4273\) |
Rank
sage: E.rank()
The elliptic curves in class 3800d have rank \(0\).
Complex multiplication
The elliptic curves in class 3800d do not have complex multiplication.Modular form 3800.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
