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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 82800d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 82800.br2 | 82800d1 | \([0, 0, 0, 825, -128250]\) | \(574992/66125\) | \(-7141500000000\) | \([2]\) | \(110592\) | \(1.1458\) | \(\Gamma_0(N)\)-optimal |
| 82800.br1 | 82800d2 | \([0, 0, 0, -33675, -2301750]\) | \(9776035692/359375\) | \(155250000000000\) | \([2]\) | \(221184\) | \(1.4924\) |
Rank
sage: E.rank()
The elliptic curves in class 82800d have rank \(1\).
Complex multiplication
The elliptic curves in class 82800d do not have complex multiplication.Modular form 82800.2.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.
