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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 44880.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44880.bw1 | 44880ch4 | \([0, 1, 0, -191496, -32318220]\) | \(189602977175292169/1402500\) | \(5744640000\) | \([2]\) | \(196608\) | \(1.4676\) | |
| 44880.bw2 | 44880ch3 | \([0, 1, 0, -16776, -67596]\) | \(127483771761289/73369857660\) | \(300522936975360\) | \([2]\) | \(196608\) | \(1.4676\) | |
| 44880.bw3 | 44880ch2 | \([0, 1, 0, -11976, -507276]\) | \(46380496070089/125888400\) | \(515638886400\) | \([2, 2]\) | \(98304\) | \(1.1211\) | |
| 44880.bw4 | 44880ch1 | \([0, 1, 0, -456, -14220]\) | \(-2565726409/19388160\) | \(-79413903360\) | \([2]\) | \(49152\) | \(0.77449\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44880.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 44880.bw do not have complex multiplication.Modular form 44880.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
