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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 95370.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 95370.bc1 | 95370x4 | \([1, 0, 1, -108926274, 424594411366]\) | \(5921450764096952391481/200074809015963750\) | \(4829319507784647117123750\) | \([2]\) | \(21233664\) | \(3.5087\) | |
| 95370.bc2 | 95370x2 | \([1, 0, 1, -16807524, -17354503634]\) | \(21754112339458491481/7199734626562500\) | \(173784091330341576562500\) | \([2, 2]\) | \(10616832\) | \(3.1622\) | |
| 95370.bc3 | 95370x1 | \([1, 0, 1, -15137104, -22665102898]\) | \(15891267085572193561/3334993530000\) | \(80498636444928570000\) | \([2]\) | \(5308416\) | \(2.8156\) | \(\Gamma_0(N)\)-optimal |
| 95370.bc4 | 95370x3 | \([1, 0, 1, 48584506, -119418384058]\) | \(525440531549759128199/559322204589843750\) | \(-13500678306519470214843750\) | \([2]\) | \(21233664\) | \(3.5087\) |
Rank
sage: E.rank()
The elliptic curves in class 95370.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 95370.bc do not have complex multiplication.Modular form 95370.2.a.bc
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.
