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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 44880.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44880.x1 | 44880bz4 | \([0, -1, 0, -38677640, 69598928112]\) | \(1562225332123379392365961/393363080510106009600\) | \(1611215177769394215321600\) | \([2]\) | \(6635520\) | \(3.3548\) | |
| 44880.x2 | 44880bz2 | \([0, -1, 0, -13279640, -18615241488]\) | \(63229930193881628103961/26218934428500000\) | \(107392755419136000000\) | \([2]\) | \(2211840\) | \(2.8055\) | |
| 44880.x3 | 44880bz1 | \([0, -1, 0, -702360, -383216400]\) | \(-9354997870579612441/10093752054144000\) | \(-41344008413773824000\) | \([2]\) | \(1105920\) | \(2.4589\) | \(\Gamma_0(N)\)-optimal |
| 44880.x4 | 44880bz3 | \([0, -1, 0, 5886840, 6923443440]\) | \(5508208700580085578359/8246033269590589440\) | \(-33775752272243054346240\) | \([2]\) | \(3317760\) | \(3.0082\) |
Rank
sage: E.rank()
The elliptic curves in class 44880.x have rank \(1\).
Complex multiplication
The elliptic curves in class 44880.x do not have complex multiplication.Modular form 44880.2.a.x
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
