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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 141610.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141610.n1 | 141610ca2 | \([1, 1, 0, -313503593, -2136674915003]\) | \(-58798411541899527001/196520000\) | \(-11389179658771880000\) | \([]\) | \(19906560\) | \(3.3025\) | |
141610.n2 | 141610ca1 | \([1, 1, 0, -3731718, -3152103128]\) | \(-99166425177001/16601562500\) | \(-962131986204101562500\) | \([]\) | \(6635520\) | \(2.7532\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141610.n have rank \(1\).
Complex multiplication
The elliptic curves in class 141610.n do not have complex multiplication.Modular form 141610.2.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.