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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 46.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46.a1 | 46a2 | \([1, -1, 0, -170, -812]\) | \(545138290809/16928\) | \(16928\) | \([2]\) | \(10\) | \(-0.091908\) | |
46.a2 | 46a1 | \([1, -1, 0, -10, -12]\) | \(-116930169/23552\) | \(-23552\) | \([2]\) | \(5\) | \(-0.43848\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46.a have rank \(0\).
Complex multiplication
The elliptic curves in class 46.a do not have complex multiplication.Modular form 46.2.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.