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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 9792.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9792.l1 | 9792bq5 | \([0, 0, 0, -15980556, -24588721136]\) | \(2361739090258884097/5202\) | \(994117681152\) | \([2]\) | \(196608\) | \(2.4361\) | |
9792.l2 | 9792bq3 | \([0, 0, 0, -998796, -384189680]\) | \(576615941610337/27060804\) | \(5171400177352704\) | \([2, 2]\) | \(98304\) | \(2.0895\) | |
9792.l3 | 9792bq6 | \([0, 0, 0, -946956, -425848304]\) | \(-491411892194497/125563633938\) | \(-23995584122926399488\) | \([2]\) | \(196608\) | \(2.4361\) | |
9792.l4 | 9792bq2 | \([0, 0, 0, -65676, -5342960]\) | \(163936758817/30338064\) | \(5797694316478464\) | \([2, 2]\) | \(49152\) | \(1.7430\) | |
9792.l5 | 9792bq1 | \([0, 0, 0, -19596, 979216]\) | \(4354703137/352512\) | \(67366092275712\) | \([2]\) | \(24576\) | \(1.3964\) | \(\Gamma_0(N)\)-optimal |
9792.l6 | 9792bq4 | \([0, 0, 0, 130164, -31115504]\) | \(1276229915423/2927177028\) | \(-559392241329635328\) | \([2]\) | \(98304\) | \(2.0895\) |
Rank
sage: E.rank()
The elliptic curves in class 9792.l have rank \(1\).
Complex multiplication
The elliptic curves in class 9792.l do not have complex multiplication.Modular form 9792.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.