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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 33800.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33800.e1 | 33800u1 | \([0, 1, 0, -85908, -9569312]\) | \(3631696/65\) | \(1254970340000000\) | \([2]\) | \(129024\) | \(1.6929\) | \(\Gamma_0(N)\)-optimal |
33800.e2 | 33800u2 | \([0, 1, 0, -1408, -27483312]\) | \(-4/4225\) | \(-326292288400000000\) | \([2]\) | \(258048\) | \(2.0394\) |
Rank
sage: E.rank()
The elliptic curves in class 33800.e have rank \(2\).
Complex multiplication
The elliptic curves in class 33800.e do not have complex multiplication.Modular form 33800.2.a.e
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.