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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 10647a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10647.g1 | 10647a1 | \([1, -1, 0, -792, 6995]\) | \(421875/91\) | \(11859469713\) | \([2]\) | \(5376\) | \(0.64708\) | \(\Gamma_0(N)\)-optimal |
| 10647.g2 | 10647a2 | \([1, -1, 0, 1743, 40964]\) | \(4492125/8281\) | \(-1079211743883\) | \([2]\) | \(10752\) | \(0.99365\) |
Rank
sage: E.rank()
The elliptic curves in class 10647a have rank \(0\).
Complex multiplication
The elliptic curves in class 10647a do not have complex multiplication.Modular form 10647.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
