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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 19494w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19494.c3 | 19494w1 | \([1, -1, 0, 474, 2668]\) | \(9261/8\) | \(-10161910296\) | \([]\) | \(14256\) | \(0.60771\) | \(\Gamma_0(N)\)-optimal |
| 19494.c2 | 19494w2 | \([1, -1, 0, -4941, -176027]\) | \(-1167051/512\) | \(-5853260330496\) | \([]\) | \(42768\) | \(1.1570\) | |
| 19494.c1 | 19494w3 | \([1, -1, 0, -10356, 413486]\) | \(-132651/2\) | \(-1852008151446\) | \([]\) | \(42768\) | \(1.1570\) |
Rank
sage: E.rank()
The elliptic curves in class 19494w have rank \(1\).
Complex multiplication
The elliptic curves in class 19494w do not have complex multiplication.Modular form 19494.2.a.w
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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
