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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 135252.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
135252.b1 | 135252a2 | \([0, 0, 0, -52887, 4077790]\) | \(3631696/507\) | \(2283857386267392\) | \([2]\) | \(983040\) | \(1.6734\) | |
135252.b2 | 135252a1 | \([0, 0, 0, -13872, -564995]\) | \(1048576/117\) | \(32940250763472\) | \([2]\) | \(491520\) | \(1.3268\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 135252.b have rank \(0\).
Complex multiplication
The elliptic curves in class 135252.b do not have complex multiplication.Modular form 135252.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.