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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 36518a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36518.a2 | 36518a1 | \([1, 1, 0, -14915, -707579]\) | \(-413493625/152\) | \(-134900559512\) | \([]\) | \(60480\) | \(1.1036\) | \(\Gamma_0(N)\)-optimal |
36518.a3 | 36518a2 | \([1, 1, 0, 9110, -2661292]\) | \(94196375/3511808\) | \(-3116742526965248\) | \([]\) | \(181440\) | \(1.6529\) | |
36518.a1 | 36518a3 | \([1, 1, 0, -82185, 72912709]\) | \(-69173457625/2550136832\) | \(-2263255825453678592\) | \([]\) | \(544320\) | \(2.2022\) |
Rank
sage: E.rank()
The elliptic curves in class 36518a have rank \(1\).
Complex multiplication
The elliptic curves in class 36518a do not have complex multiplication.Modular form 36518.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.