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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 93058.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93058.a1 | 93058b2 | \([1, 0, 1, -174996, 26364434]\) | \(24553362849625/1755162752\) | \(42365362032629888\) | \([2]\) | \(1032192\) | \(1.9374\) | |
93058.a2 | 93058b1 | \([1, 0, 1, 9964, 1801746]\) | \(4533086375/60669952\) | \(-1464425152626688\) | \([2]\) | \(516096\) | \(1.5908\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 93058.a have rank \(2\).
Complex multiplication
The elliptic curves in class 93058.a do not have complex multiplication.Modular form 93058.2.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.