Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 107800i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107800.be4 | 107800i1 | \([0, 0, 0, -57575, -13119750]\) | \(-44851536/132055\) | \(-62144554780000000\) | \([2]\) | \(589824\) | \(1.9093\) | \(\Gamma_0(N)\)-optimal |
| 107800.be3 | 107800i2 | \([0, 0, 0, -1258075, -542540250]\) | \(116986321764/148225\) | \(279016368400000000\) | \([2, 2]\) | \(1179648\) | \(2.2558\) | |
| 107800.be2 | 107800i3 | \([0, 0, 0, -1601075, -223207250]\) | \(120564797922/64054375\) | \(241149861260000000000\) | \([2]\) | \(2359296\) | \(2.6024\) | |
| 107800.be1 | 107800i4 | \([0, 0, 0, -20123075, -34744785250]\) | \(239369344910082/385\) | \(1449435680000000\) | \([2]\) | \(2359296\) | \(2.6024\) |
Rank
sage: E.rank()
The elliptic curves in class 107800i have rank \(0\).
Complex multiplication
The elliptic curves in class 107800i do not have complex multiplication.Modular form 107800.2.a.i
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.
