Show commands:
SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 338130.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338130.ca1 | 338130ca3 | \([1, -1, 0, -981383364, 11833547635728]\) | \(5940441603429810927841/3044264109120\) | \(53567747406330388845120\) | \([2]\) | \(169869312\) | \(3.6935\) | |
| 338130.ca2 | 338130ca2 | \([1, -1, 0, -61669764, 182799693648]\) | \(1474074790091785441/32813650022400\) | \(577398429595440496742400\) | \([2, 2]\) | \(84934656\) | \(3.3469\) | |
| 338130.ca3 | 338130ca1 | \([1, -1, 0, -8401284, -5163464880]\) | \(3726830856733921/1501644718080\) | \(26423372634187188142080\) | \([2]\) | \(42467328\) | \(3.0003\) | \(\Gamma_0(N)\)-optimal |
| 338130.ca4 | 338130ca4 | \([1, -1, 0, 5748156, 561054675600]\) | \(1193680917131039/7728836230440000\) | \(-135998826677618196862440000\) | \([2]\) | \(169869312\) | \(3.6935\) |
Rank
sage: E.rank()
The elliptic curves in class 338130.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 338130.ca do not have complex multiplication.Modular form 338130.2.a.ca
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.
