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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2601.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2601.c1 | 2601k2 | \([0, 0, 1, -2196111, 1252668838]\) | \(-13549359104/243\) | \(-21007486557814059\) | \([]\) | \(65280\) | \(2.2588\) | |
2601.c2 | 2601k1 | \([0, 0, 1, 14739, 354964]\) | \(4096/3\) | \(-259351685898939\) | \([]\) | \(13056\) | \(1.4541\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2601.c have rank \(0\).
Complex multiplication
The elliptic curves in class 2601.c do not have complex multiplication.Modular form 2601.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.