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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 1110.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1110.n1 | 1110n2 | \([1, 0, 0, -7364036, -7692307440]\) | \(-44164307457093068844199489/1823508000000000\) | \(-1823508000000000\) | \([]\) | \(23760\) | \(2.4147\) | |
1110.n2 | 1110n1 | \([1, 0, 0, -83396, -12375024]\) | \(-64144540676215729729/28962038218752000\) | \(-28962038218752000\) | \([3]\) | \(7920\) | \(1.8654\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1110.n have rank \(0\).
Complex multiplication
The elliptic curves in class 1110.n do not have complex multiplication.Modular form 1110.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.