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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 110561a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
110561.b1 | 110561a1 | \([0, 1, 1, -14459, -787451]\) | \(-2258403328/480491\) | \(-71129912341499\) | \([]\) | \(299376\) | \(1.3793\) | \(\Gamma_0(N)\)-optimal |
110561.b2 | 110561a2 | \([0, 1, 1, 101921, 4560210]\) | \(790939860992/517504691\) | \(-76609266993855299\) | \([]\) | \(898128\) | \(1.9286\) |
Rank
sage: E.rank()
The elliptic curves in class 110561a have rank \(0\).
Complex multiplication
The elliptic curves in class 110561a do not have complex multiplication.Modular form 110561.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.