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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 61152bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 61152.ca3 | 61152bt1 | \([0, 1, 0, -11482, 467480]\) | \(22235451328/123201\) | \(927646364736\) | \([2, 2]\) | \(147456\) | \(1.1391\) | \(\Gamma_0(N)\)-optimal |
| 61152.ca4 | 61152bt2 | \([0, 1, 0, -5112, 989820]\) | \(-245314376/6908733\) | \(-416156430703104\) | \([2]\) | \(294912\) | \(1.4857\) | |
| 61152.ca2 | 61152bt3 | \([0, 1, 0, -18097, -139777]\) | \(1360251712/771147\) | \(371608262258688\) | \([2]\) | \(294912\) | \(1.4857\) | |
| 61152.ca1 | 61152bt4 | \([0, 1, 0, -183472, 30187352]\) | \(11339065490696/351\) | \(21142937088\) | \([2]\) | \(294912\) | \(1.4857\) |
Rank
sage: E.rank()
The elliptic curves in class 61152bt have rank \(0\).
Complex multiplication
The elliptic curves in class 61152bt do not have complex multiplication.Modular form 61152.2.a.bt
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
