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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 2646.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2646.x1 | 2646w1 | \([1, -1, 1, -965, -11539]\) | \(-637875/16\) | \(-2490394032\) | \([]\) | \(2016\) | \(0.58732\) | \(\Gamma_0(N)\)-optimal |
2646.x2 | 2646w2 | \([1, -1, 1, 4180, -50641]\) | \(5767125/4096\) | \(-5737867849728\) | \([3]\) | \(6048\) | \(1.1366\) |
Rank
sage: E.rank()
The elliptic curves in class 2646.x have rank \(1\).
Complex multiplication
The elliptic curves in class 2646.x do not have complex multiplication.Modular form 2646.2.a.x
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.