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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2601.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2601.a1 | 2601l2 | \([0, 0, 1, -7599, 254970]\) | \(-13549359104/243\) | \(-870323211\) | \([]\) | \(3840\) | \(0.84218\) | |
2601.a2 | 2601l1 | \([0, 0, 1, 51, 72]\) | \(4096/3\) | \(-10744731\) | \([]\) | \(768\) | \(0.037462\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2601.a have rank \(2\).
Complex multiplication
The elliptic curves in class 2601.a do not have complex multiplication.Modular form 2601.2.a.a
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.