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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 11376n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11376.d3 | 11376n1 | \([0, 0, 0, -6699, 211034]\) | \(11134383337/316\) | \(943570944\) | \([]\) | \(9600\) | \(0.82370\) | \(\Gamma_0(N)\)-optimal |
| 11376.d2 | 11376n2 | \([0, 0, 0, -11739, -146806]\) | \(59914169497/31554496\) | \(94221220184064\) | \([]\) | \(28800\) | \(1.3730\) | |
| 11376.d1 | 11376n3 | \([0, 0, 0, -751179, -250589446]\) | \(15698803397448457/20709376\) | \(61837865385984\) | \([]\) | \(86400\) | \(1.9223\) |
Rank
sage: E.rank()
The elliptic curves in class 11376n have rank \(1\).
Complex multiplication
The elliptic curves in class 11376n do not have complex multiplication.Modular form 11376.2.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.
