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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 13872.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13872.c1 | 13872bb2 | \([0, -1, 0, -601693472, 5681021020416]\) | \(-843137281012581793/216\) | \(-6171703735320576\) | \([]\) | \(2776032\) | \(3.3123\) | |
13872.c2 | 13872bb1 | \([0, -1, 0, -7416992, 7820031744]\) | \(-1579268174113/10077696\) | \(-287947009475116793856\) | \([]\) | \(925344\) | \(2.7630\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13872.c have rank \(1\).
Complex multiplication
The elliptic curves in class 13872.c do not have complex multiplication.Modular form 13872.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.