Show commands:
SageMath
E = EllipticCurve("fo1")
E.isogeny_class()
Elliptic curves in class 185130.fo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185130.fo1 | 185130ca4 | \([1, -1, 1, -6280440167, 191574101218591]\) | \(785681552361835673854227/2604236800\) | \(90808787094058598400\) | \([2]\) | \(116121600\) | \(3.9357\) | |
| 185130.fo2 | 185130ca3 | \([1, -1, 1, -392522087, 2993505785119]\) | \(-191808834096148160787/11043434659840\) | \(-385080537535049807953920\) | \([2]\) | \(58060800\) | \(3.5891\) | |
| 185130.fo3 | 185130ca2 | \([1, -1, 1, -77813792, 260831830691]\) | \(1089365384367428097483/16063552169500000\) | \(768354188713692916500000\) | \([2]\) | \(38707200\) | \(3.3863\) | |
| 185130.fo4 | 185130ca1 | \([1, -1, 1, -509312, 11107438499]\) | \(-305460292990923/1114070936704000\) | \(-53288404812853423488000\) | \([2]\) | \(19353600\) | \(3.0398\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 185130.fo have rank \(0\).
Complex multiplication
The elliptic curves in class 185130.fo do not have complex multiplication.Modular form 185130.2.a.fo
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
