Show commands:
SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 176610cn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176610.u4 | 176610cn1 | \([1, 0, 1, 18715596, 82007296306]\) | \(1218840126444091871/5589443704320000\) | \(-3324731466746164446720000\) | \([2]\) | \(38707200\) | \(3.3877\) | \(\Gamma_0(N)\)-optimal |
| 176610.u3 | 176610cn2 | \([1, 0, 1, -207614324, 1024626147122]\) | \(1663825065311223487009/200359188225000000\) | \(119178317732858595225000000\) | \([2, 2]\) | \(77414400\) | \(3.7343\) | |
| 176610.u1 | 176610cn3 | \([1, 0, 1, -3219168044, 70299998679026]\) | \(6202498505128804178179489/109281005859375000\) | \(65002890827493896484375000\) | \([2]\) | \(154828800\) | \(4.0808\) | |
| 176610.u2 | 176610cn4 | \([1, 0, 1, -817339324, -7922234612878]\) | \(101517965795304671887009/13167839372235345000\) | \(7832537945787583106480745000\) | \([2]\) | \(154828800\) | \(4.0808\) |
Rank
sage: E.rank()
The elliptic curves in class 176610cn have rank \(0\).
Complex multiplication
The elliptic curves in class 176610cn do not have complex multiplication.Modular form 176610.2.a.cn
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.
