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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 2352.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2352.l1 | 2352o4 | \([0, -1, 0, -1053712, 416675008]\) | \(268498407453697/252\) | \(121436356608\) | \([4]\) | \(18432\) | \(1.8552\) | |
| 2352.l2 | 2352o5 | \([0, -1, 0, -716592, -231003072]\) | \(84448510979617/933897762\) | \(450036276435099648\) | \([2]\) | \(36864\) | \(2.2018\) | |
| 2352.l3 | 2352o3 | \([0, -1, 0, -81552, 3199680]\) | \(124475734657/63011844\) | \(30364796660760576\) | \([2, 2]\) | \(18432\) | \(1.8552\) | |
| 2352.l4 | 2352o2 | \([0, -1, 0, -65872, 6523840]\) | \(65597103937/63504\) | \(30601961865216\) | \([2, 2]\) | \(9216\) | \(1.5086\) | |
| 2352.l5 | 2352o1 | \([0, -1, 0, -3152, 151488]\) | \(-7189057/16128\) | \(-7771926822912\) | \([2]\) | \(4608\) | \(1.1621\) | \(\Gamma_0(N)\)-optimal |
| 2352.l6 | 2352o6 | \([0, -1, 0, 302608, 24405312]\) | \(6359387729183/4218578658\) | \(-2032892151951532032\) | \([2]\) | \(36864\) | \(2.2018\) |
Rank
sage: E.rank()
The elliptic curves in class 2352.l have rank \(1\).
Complex multiplication
The elliptic curves in class 2352.l do not have complex multiplication.Modular form 2352.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
