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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 14157.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14157.n1 | 14157g1 | \([0, 0, 1, -660, 6597]\) | \(-360448000/4563\) | \(-402497667\) | \([]\) | \(3840\) | \(0.46087\) | \(\Gamma_0(N)\)-optimal |
14157.n2 | 14157g2 | \([0, 0, 1, 2310, 33624]\) | \(15454208000/14480427\) | \(-1277303985243\) | \([]\) | \(11520\) | \(1.0102\) |
Rank
sage: E.rank()
The elliptic curves in class 14157.n have rank \(1\).
Complex multiplication
The elliptic curves in class 14157.n do not have complex multiplication.Modular form 14157.2.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.