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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 2601.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2601.f1 | 2601g2 | \([0, 0, 1, -154326, 23347804]\) | \(-23100424192/14739\) | \(-259351685898939\) | \([]\) | \(13824\) | \(1.7067\) | |
2601.f2 | 2601g1 | \([0, 0, 1, 1734, 133879]\) | \(32768/459\) | \(-8076696100659\) | \([]\) | \(4608\) | \(1.1574\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2601.f have rank \(0\).
Complex multiplication
The elliptic curves in class 2601.f do not have complex multiplication.Modular form 2601.2.a.f
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.