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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 252.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 252.b1 | 252a4 | \([0, 0, 0, -16455, 812446]\) | \(2640279346000/3087\) | \(576108288\) | \([6]\) | \(288\) | \(0.96412\) | |
| 252.b2 | 252a3 | \([0, 0, 0, -1020, 12913]\) | \(-10061824000/352947\) | \(-4116773808\) | \([6]\) | \(144\) | \(0.61754\) | |
| 252.b3 | 252a2 | \([0, 0, 0, -255, 502]\) | \(9826000/5103\) | \(952342272\) | \([2]\) | \(96\) | \(0.41481\) | |
| 252.b4 | 252a1 | \([0, 0, 0, 60, 61]\) | \(2048000/1323\) | \(-15431472\) | \([2]\) | \(48\) | \(0.068235\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 252.b have rank \(0\).
Complex multiplication
The elliptic curves in class 252.b do not have complex multiplication.Modular form 252.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
