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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 37440fl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37440.da4 | 37440fl1 | \([0, 0, 0, -732, 27056]\) | \(-3631696/24375\) | \(-291133440000\) | \([2]\) | \(49152\) | \(0.88311\) | \(\Gamma_0(N)\)-optimal |
| 37440.da3 | 37440fl2 | \([0, 0, 0, -18732, 984656]\) | \(15214885924/38025\) | \(1816672665600\) | \([2, 2]\) | \(98304\) | \(1.2297\) | |
| 37440.da2 | 37440fl3 | \([0, 0, 0, -25932, 158096]\) | \(20183398562/11567205\) | \(1105263649751040\) | \([2]\) | \(196608\) | \(1.5763\) | |
| 37440.da1 | 37440fl4 | \([0, 0, 0, -299532, 63097616]\) | \(31103978031362/195\) | \(18632540160\) | \([2]\) | \(196608\) | \(1.5763\) |
Rank
sage: E.rank()
The elliptic curves in class 37440fl have rank \(2\).
Complex multiplication
The elliptic curves in class 37440fl do not have complex multiplication.Modular form 37440.2.a.fl
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
