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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 262080.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
262080.c1 | 262080c3 | \([0, 0, 0, -29648748, -62138026928]\) | \(15082569606665230489/7751016000\) | \(1481242224623616000\) | \([2]\) | \(15925248\) | \(2.8187\) | |
262080.c2 | 262080c4 | \([0, 0, 0, -29487468, -62847465392]\) | \(-14837772556740428569/342100087875000\) | \(-65376344882774016000000\) | \([2]\) | \(31850496\) | \(3.1652\) | |
262080.c3 | 262080c1 | \([0, 0, 0, -436908, -49912112]\) | \(48264326765929/22299191460\) | \(4261441850399784960\) | \([2]\) | \(5308416\) | \(2.2694\) | \(\Gamma_0(N)\)-optimal |
262080.c4 | 262080c2 | \([0, 0, 0, 1538772, -376294448]\) | \(2108526614950391/1540302022350\) | \(-294356300409903513600\) | \([2]\) | \(10616832\) | \(2.6159\) |
Rank
sage: E.rank()
The elliptic curves in class 262080.c have rank \(1\).
Complex multiplication
The elliptic curves in class 262080.c do not have complex multiplication.Modular form 262080.2.a.c
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.