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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 6400i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6400.s2 | 6400i1 | \([0, 1, 0, 67, -37]\) | \(1600\) | \(-20480000\) | \([]\) | \(1152\) | \(0.091987\) | \(\Gamma_0(N)\)-optimal |
6400.s1 | 6400i2 | \([0, 1, 0, -6333, 191963]\) | \(-2194880\) | \(-12800000000\) | \([]\) | \(5760\) | \(0.89671\) |
Rank
sage: E.rank()
The elliptic curves in class 6400i have rank \(0\).
Complex multiplication
The elliptic curves in class 6400i do not have complex multiplication.Modular form 6400.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.