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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 4950.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4950.i1 | 4950f1 | \([1, -1, 0, -3117, 71541]\) | \(-317605995/21296\) | \(-224606250000\) | \([3]\) | \(5760\) | \(0.93001\) | \(\Gamma_0(N)\)-optimal |
4950.i2 | 4950f2 | \([1, -1, 0, 17508, 78416]\) | \(77191245/45056\) | \(-346420800000000\) | \([]\) | \(17280\) | \(1.4793\) |
Rank
sage: E.rank()
The elliptic curves in class 4950.i have rank \(1\).
Complex multiplication
The elliptic curves in class 4950.i do not have complex multiplication.Modular form 4950.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.