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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 218010b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 218010.ch3 | 218010b1 | \([1, 0, 0, -11580, -480000]\) | \(35578826569/51600\) | \(249063344400\) | \([2]\) | \(442368\) | \(1.0888\) | \(\Gamma_0(N)\)-optimal |
| 218010.ch2 | 218010b2 | \([1, 0, 0, -14960, -177828]\) | \(76711450249/41602500\) | \(200807321422500\) | \([2, 2]\) | \(884736\) | \(1.4354\) | |
| 218010.ch1 | 218010b3 | \([1, 0, 0, -141710, 20381022]\) | \(65202655558249/512820150\) | \(2475284915401350\) | \([2]\) | \(1769472\) | \(1.7820\) | |
| 218010.ch4 | 218010b4 | \([1, 0, 0, 57710, -1384150]\) | \(4403686064471/2721093750\) | \(-13134199802343750\) | \([2]\) | \(1769472\) | \(1.7820\) |
Rank
sage: E.rank()
The elliptic curves in class 218010b have rank \(0\).
Complex multiplication
The elliptic curves in class 218010b do not have complex multiplication.Modular form 218010.2.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 Cremona 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 Cremona labels.
