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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 61936n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61936.t3 | 61936n1 | \([0, 1, 0, -36472, 2668756]\) | \(11134383337/316\) | \(152277336064\) | \([]\) | \(120960\) | \(1.2473\) | \(\Gamma_0(N)\)-optimal |
61936.t2 | 61936n2 | \([0, 1, 0, -63912, -1886284]\) | \(59914169497/31554496\) | \(15205805670006784\) | \([]\) | \(362880\) | \(1.7967\) | |
61936.t1 | 61936n3 | \([0, 1, 0, -4089752, -3184777324]\) | \(15698803397448457/20709376\) | \(9979647496290304\) | \([]\) | \(1088640\) | \(2.3460\) |
Rank
sage: E.rank()
The elliptic curves in class 61936n have rank \(1\).
Complex multiplication
The elliptic curves in class 61936n do not have complex multiplication.Modular form 61936.2.a.n
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.