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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 24882.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24882.c1 | 24882g4 | \([1, 1, 0, -1150101, 474257025]\) | \(168241156610234677286617/17467164\) | \(17467164\) | \([2]\) | \(159744\) | \(1.7349\) | |
24882.c2 | 24882g2 | \([1, 1, 0, -71881, 7387765]\) | \(41074802461509814297/418521012624\) | \(418521012624\) | \([2, 2]\) | \(79872\) | \(1.3883\) | |
24882.c3 | 24882g3 | \([1, 1, 0, -70141, 7764649]\) | \(-38163592211939879257/4156203493184028\) | \(-4156203493184028\) | \([2]\) | \(159744\) | \(1.7349\) | |
24882.c4 | 24882g1 | \([1, 1, 0, -4601, 108069]\) | \(10775263270478617/1009793571072\) | \(1009793571072\) | \([2]\) | \(39936\) | \(1.0418\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24882.c have rank \(1\).
Complex multiplication
The elliptic curves in class 24882.c do not have complex multiplication.Modular form 24882.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.