Show commands:
SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 235950.cd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235950.cd1 | 235950cd4 | \([1, 1, 0, -261748775, -1630062136875]\) | \(71647584155243142409/10140000\) | \(280681695937500000\) | \([2]\) | \(44236800\) | \(3.2009\) | |
| 235950.cd2 | 235950cd3 | \([1, 1, 0, -18780775, -17442864875]\) | \(26465989780414729/10571870144160\) | \(292636138194659902500000\) | \([2]\) | \(44236800\) | \(3.2009\) | |
| 235950.cd3 | 235950cd2 | \([1, 1, 0, -16360775, -25470004875]\) | \(17496824387403529/6580454400\) | \(182151193395600000000\) | \([2, 2]\) | \(22118400\) | \(2.8544\) | |
| 235950.cd4 | 235950cd1 | \([1, 1, 0, -872775, -518836875]\) | \(-2656166199049/2658140160\) | \(-73579022499840000000\) | \([2]\) | \(11059200\) | \(2.5078\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235950.cd have rank \(0\).
Complex multiplication
The elliptic curves in class 235950.cd do not have complex multiplication.Modular form 235950.2.a.cd
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
