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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 10982.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10982.a1 | 10982b3 | \([1, 1, 0, -24715, -12040387]\) | \(-69173457625/2550136832\) | \(-61554103741841408\) | \([]\) | \(90720\) | \(1.9018\) | |
10982.a2 | 10982b1 | \([1, 1, 0, -4485, 113797]\) | \(-413493625/152\) | \(-3668910488\) | \([]\) | \(10080\) | \(0.80316\) | \(\Gamma_0(N)\)-optimal |
10982.a3 | 10982b2 | \([1, 1, 0, 2740, 440656]\) | \(94196375/3511808\) | \(-84766507914752\) | \([]\) | \(30240\) | \(1.3525\) |
Rank
sage: E.rank()
The elliptic curves in class 10982.a have rank \(0\).
Complex multiplication
The elliptic curves in class 10982.a do not have complex multiplication.Modular form 10982.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.