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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 4290i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4290.h2 | 4290i1 | \([1, 1, 0, 74288, -2411264]\) | \(45338857965533777399/28814396538470400\) | \(-28814396538470400\) | \([2]\) | \(37632\) | \(1.8473\) | \(\Gamma_0(N)\)-optimal |
4290.h1 | 4290i2 | \([1, 1, 0, -312912, -20145024]\) | \(3388383326345613179401/1787816842064922240\) | \(1787816842064922240\) | \([2]\) | \(75264\) | \(2.1939\) |
Rank
sage: E.rank()
The elliptic curves in class 4290i have rank \(1\).
Complex multiplication
The elliptic curves in class 4290i do not have complex multiplication.Modular form 4290.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.