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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 24299c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24299.a3 | 24299c1 | \([0, -1, 1, -736, -18020]\) | \(-4096/11\) | \(-118571368619\) | \([]\) | \(20608\) | \(0.81234\) | \(\Gamma_0(N)\)-optimal |
24299.a2 | 24299c2 | \([0, -1, 1, -22826, 2411880]\) | \(-122023936/161051\) | \(-1736003407950779\) | \([]\) | \(103040\) | \(1.6171\) | |
24299.a1 | 24299c3 | \([0, -1, 1, -17275116, 27642038400]\) | \(-52893159101157376/11\) | \(-118571368619\) | \([]\) | \(515200\) | \(2.4218\) |
Rank
sage: E.rank()
The elliptic curves in class 24299c have rank \(2\).
Complex multiplication
The elliptic curves in class 24299c do not have complex multiplication.Modular form 24299.2.a.c
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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.