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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 426888.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
426888.a1 | 426888a2 | \([0, 0, 0, -72588747, -7181264090]\) | \(102129622/59049\) | \(24456394672174163769219072\) | \([2]\) | \(145981440\) | \(3.5611\) | |
426888.a2 | 426888a1 | \([0, 0, 0, -49109907, 132024778270]\) | \(63253004/243\) | \(50321799736983876068352\) | \([2]\) | \(72990720\) | \(3.2145\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 426888.a have rank \(0\).
Complex multiplication
The elliptic curves in class 426888.a do not have complex multiplication.Modular form 426888.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.