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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 36400.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 36400.l1 | 36400by4 | \([0, 1, 0, -5867408, 5468327188]\) | \(349046010201856969/7245875000\) | \(463736000000000000\) | \([2]\) | \(995328\) | \(2.5086\) | |
| 36400.l2 | 36400by3 | \([0, 1, 0, -379408, 79111188]\) | \(94376601570889/12235496000\) | \(783071744000000000\) | \([2]\) | \(497664\) | \(2.1620\) | |
| 36400.l3 | 36400by2 | \([0, 1, 0, -121408, -3892812]\) | \(3092354182009/1689383150\) | \(108120521600000000\) | \([2]\) | \(331776\) | \(1.9593\) | |
| 36400.l4 | 36400by1 | \([0, 1, 0, -93408, -11004812]\) | \(1408317602329/2153060\) | \(137795840000000\) | \([2]\) | \(165888\) | \(1.6127\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 36400.l have rank \(1\).
Complex multiplication
The elliptic curves in class 36400.l do not have complex multiplication.Modular form 36400.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
