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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 134657.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 134657.b1 | 134657b4 | \([1, -1, 1, -718336, -234156518]\) | \(82483294977/17\) | \(8448681946337\) | \([2]\) | \(704000\) | \(1.8677\) | |
| 134657.b2 | 134657b2 | \([1, -1, 1, -45051, -3623734]\) | \(20346417/289\) | \(143627593087729\) | \([2, 2]\) | \(352000\) | \(1.5211\) | |
| 134657.b3 | 134657b3 | \([1, -1, 1, -5446, -9802114]\) | \(-35937/83521\) | \(-41508374402353681\) | \([2]\) | \(704000\) | \(1.8677\) | |
| 134657.b4 | 134657b1 | \([1, -1, 1, -5446, 67452]\) | \(35937/17\) | \(8448681946337\) | \([2]\) | \(176000\) | \(1.1745\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 134657.b have rank \(0\).
Complex multiplication
The elliptic curves in class 134657.b do not have complex multiplication.Modular form 134657.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
