Show commands:
SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 170352cn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 170352.fv3 | 170352cn1 | \([0, 0, 0, 328029, 687630242]\) | \(270840023/14329224\) | \(-206523873484683116544\) | \([]\) | \(6967296\) | \(2.5778\) | \(\Gamma_0(N)\)-optimal |
| 170352.fv2 | 170352cn2 | \([0, 0, 0, -2957331, -18745274158]\) | \(-198461344537/10417365504\) | \(-150143139320859117748224\) | \([]\) | \(20901888\) | \(3.1271\) | |
| 170352.fv1 | 170352cn3 | \([0, 0, 0, -634111491, -6146155952638]\) | \(-1956469094246217097/36641439744\) | \(-528104806372382462705664\) | \([]\) | \(62705664\) | \(3.6764\) |
Rank
sage: E.rank()
The elliptic curves in class 170352cn have rank \(0\).
Complex multiplication
The elliptic curves in class 170352cn do not have complex multiplication.Modular form 170352.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
