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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 5056.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5056.l1 | 5056n3 | \([0, 1, 0, -333857, 74137439]\) | \(15698803397448457/20709376\) | \(5428838662144\) | \([]\) | \(23040\) | \(1.7196\) | |
5056.l2 | 5056n2 | \([0, 1, 0, -5217, 41759]\) | \(59914169497/31554496\) | \(8271821799424\) | \([]\) | \(7680\) | \(1.1703\) | |
5056.l3 | 5056n1 | \([0, 1, 0, -2977, -63521]\) | \(11134383337/316\) | \(82837504\) | \([]\) | \(2560\) | \(0.62097\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5056.l have rank \(0\).
Complex multiplication
The elliptic curves in class 5056.l do not have complex multiplication.Modular form 5056.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.