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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 799.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
799.a1 | 799b2 | \([1, 1, 1, -353, -2120]\) | \(4865469108625/1134465743\) | \(1134465743\) | \([2]\) | \(336\) | \(0.44939\) | |
799.a2 | 799b1 | \([1, 1, 1, -118, 418]\) | \(181802454625/10852817\) | \(10852817\) | \([2]\) | \(168\) | \(0.10282\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 799.a have rank \(1\).
Complex multiplication
The elliptic curves in class 799.a do not have complex multiplication.Modular form 799.2.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.