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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1014.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1014.b1 | 1014c4 | \([1, 0, 1, -70997, 7275296]\) | \(18013780041269221/9216\) | \(20247552\) | \([2]\) | \(2400\) | \(1.1700\) | |
| 1014.b2 | 1014c3 | \([1, 0, 1, -4437, 113440]\) | \(-4395631034341/3145728\) | \(-6911164416\) | \([2]\) | \(1200\) | \(0.82343\) | |
| 1014.b3 | 1014c2 | \([1, 0, 1, -212, -466]\) | \(476379541/236196\) | \(518922612\) | \([2]\) | \(480\) | \(0.36529\) | |
| 1014.b4 | 1014c1 | \([1, 0, 1, 48, -50]\) | \(5735339/3888\) | \(-8541936\) | \([2]\) | \(240\) | \(0.018713\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1014.b have rank \(1\).
Complex multiplication
The elliptic curves in class 1014.b do not have complex multiplication.Modular form 1014.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
