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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 4790.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4790.b1 | 4790c2 | \([1, 1, 1, -9155, -1568583]\) | \(-84859745100243121/1008643184735960\) | \(-1008643184735960\) | \([]\) | \(18000\) | \(1.5608\) | |
4790.b2 | 4790c1 | \([1, 1, 1, -955, 15177]\) | \(-96330152758321/49049600000\) | \(-49049600000\) | \([5]\) | \(3600\) | \(0.75609\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4790.b have rank \(1\).
Complex multiplication
The elliptic curves in class 4790.b do not have complex multiplication.Modular form 4790.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.