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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 2646.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2646.n1 | 2646f1 | \([1, -1, 0, -6918, -219752]\) | \(-11527859979/28\) | \(-88942644\) | \([]\) | \(3456\) | \(0.76559\) | \(\Gamma_0(N)\)-optimal |
2646.n2 | 2646f2 | \([1, -1, 0, -4713, -363763]\) | \(-5000211/21952\) | \(-50833922981184\) | \([]\) | \(10368\) | \(1.3149\) | |
2646.n3 | 2646f3 | \([1, -1, 0, 41592, 8813888]\) | \(381790581/1835008\) | \(-38243708913844224\) | \([]\) | \(31104\) | \(1.8642\) |
Rank
sage: E.rank()
The elliptic curves in class 2646.n have rank \(0\).
Complex multiplication
The elliptic curves in class 2646.n do not have complex multiplication.Modular form 2646.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.