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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 8470.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8470.b1 | 8470e1 | \([1, 0, 1, -179, -2994]\) | \(-5200020529/28672000\) | \(-3469312000\) | \([]\) | \(6480\) | \(0.51463\) | \(\Gamma_0(N)\)-optimal |
8470.b2 | 8470e2 | \([1, 0, 1, 1581, 73742]\) | \(3615170357711/21437500000\) | \(-2593937500000\) | \([]\) | \(19440\) | \(1.0639\) |
Rank
sage: E.rank()
The elliptic curves in class 8470.b have rank \(0\).
Complex multiplication
The elliptic curves in class 8470.b do not have complex multiplication.Modular form 8470.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.