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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 35322.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35322.a1 | 35322f2 | \([1, 1, 0, -206062, -23220830]\) | \(1626794704081/552715002\) | \(328767773056161642\) | \([2]\) | \(967680\) | \(2.0633\) | |
35322.a2 | 35322f1 | \([1, 1, 0, 37828, -2490180]\) | \(10063705679/10384668\) | \(-6177042707242428\) | \([2]\) | \(483840\) | \(1.7168\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35322.a have rank \(1\).
Complex multiplication
The elliptic curves in class 35322.a do not have complex multiplication.Modular form 35322.2.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.