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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 250470.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 250470.d1 | 250470d3 | \([1, -1, 0, -384724665, 2904608073901]\) | \(4876297165069215549481/969819840\) | \(1252491259060704960\) | \([2]\) | \(58982400\) | \(3.3030\) | |
| 250470.d2 | 250470d2 | \([1, -1, 0, -24047865, 45378809581]\) | \(1190884543636720681/530916249600\) | \(685661330580009062400\) | \([2, 2]\) | \(29491200\) | \(2.9564\) | |
| 250470.d3 | 250470d4 | \([1, -1, 0, -20214585, 60327834925]\) | \(-707350352645673001/807856192440000\) | \(-1043320396094559954360000\) | \([2]\) | \(58982400\) | \(3.3030\) | |
| 250470.d4 | 250470d1 | \([1, -1, 0, -1745145, 465592045]\) | \(455129268177961/191008604160\) | \(246681494076040151040\) | \([2]\) | \(14745600\) | \(2.6099\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 250470.d have rank \(2\).
Complex multiplication
The elliptic curves in class 250470.d do not have complex multiplication.Modular form 250470.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
