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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 800.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
800.i1 | 800g1 | \([0, -1, 0, -158, 812]\) | \(438976/5\) | \(5000000\) | \([2]\) | \(192\) | \(0.098674\) | \(\Gamma_0(N)\)-optimal |
800.i2 | 800g2 | \([0, -1, 0, -33, 1937]\) | \(-64/25\) | \(-1600000000\) | \([2]\) | \(384\) | \(0.44525\) |
Rank
sage: E.rank()
The elliptic curves in class 800.i have rank \(0\).
Complex multiplication
The elliptic curves in class 800.i do not have complex multiplication.Modular form 800.2.a.i
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.