Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 13950.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13950.bw1 | 13950cp4 | \([1, -1, 1, -142980980, 658095753147]\) | \(28379906689597370652529/1357352437500\) | \(15461092608398437500\) | \([2]\) | \(1658880\) | \(3.1593\) | |
| 13950.bw2 | 13950cp3 | \([1, -1, 1, -8921480, 10320249147]\) | \(-6894246873502147249/47925198774000\) | \(-545897967285093750000\) | \([2]\) | \(829440\) | \(2.8128\) | |
| 13950.bw3 | 13950cp2 | \([1, -1, 1, -1919480, 736041147]\) | \(68663623745397169/19216056254400\) | \(218882890772775000000\) | \([2]\) | \(552960\) | \(2.6100\) | |
| 13950.bw4 | 13950cp1 | \([1, -1, 1, 312520, 75369147]\) | \(296354077829711/387386634240\) | \(-4412575880640000000\) | \([2]\) | \(276480\) | \(2.2635\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13950.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 13950.bw do not have complex multiplication.Modular form 13950.2.a.bw
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
