Show commands:
SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 274890.ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 274890.ct1 | 274890ct4 | \([1, 0, 1, -586458, -172912232]\) | \(189602977175292169/1402500\) | \(165002722500\) | \([2]\) | \(3145728\) | \(1.7474\) | |
| 274890.ct2 | 274890ct3 | \([1, 0, 1, -51378, -336584]\) | \(127483771761289/73369857660\) | \(8631890383841340\) | \([2]\) | \(3145728\) | \(1.7474\) | |
| 274890.ct3 | 274890ct2 | \([1, 0, 1, -36678, -2700344]\) | \(46380496070089/125888400\) | \(14810644371600\) | \([2, 2]\) | \(1572864\) | \(1.4009\) | |
| 274890.ct4 | 274890ct1 | \([1, 0, 1, -1398, -75512]\) | \(-2565726409/19388160\) | \(-2280997635840\) | \([2]\) | \(786432\) | \(1.0543\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 274890.ct have rank \(1\).
Complex multiplication
The elliptic curves in class 274890.ct do not have complex multiplication.Modular form 274890.2.a.ct
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.
