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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 4854.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4854.b1 | 4854c2 | \([1, 0, 0, -47760, -8600184]\) | \(-12048063138901520641/24950261657019528\) | \(-24950261657019528\) | \([]\) | \(72000\) | \(1.8355\) | |
4854.b2 | 4854c1 | \([1, 0, 0, -2040, 69696]\) | \(-938917686360961/1565348364288\) | \(-1565348364288\) | \([5]\) | \(14400\) | \(1.0307\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4854.b have rank \(1\).
Complex multiplication
The elliptic curves in class 4854.b do not have complex multiplication.Modular form 4854.2.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.