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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 9338.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9338.a1 | 9338e2 | \([1, 0, 1, -542, -4500]\) | \(17561807821657/1590616244\) | \(1590616244\) | \([2]\) | \(5120\) | \(0.50503\) | |
9338.a2 | 9338e1 | \([1, 0, 1, 38, -324]\) | \(6300872423/49827568\) | \(-49827568\) | \([2]\) | \(2560\) | \(0.15846\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9338.a have rank \(1\).
Complex multiplication
The elliptic curves in class 9338.a do not have complex multiplication.Modular form 9338.2.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.