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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 181944bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 181944.e3 | 181944bj1 | \([0, 0, 0, -23826, -1406095]\) | \(2725888/21\) | \(11523606275664\) | \([2]\) | \(442368\) | \(1.3353\) | \(\Gamma_0(N)\)-optimal |
| 181944.e2 | 181944bj2 | \([0, 0, 0, -40071, 754490]\) | \(810448/441\) | \(3871931708623104\) | \([2, 2]\) | \(884736\) | \(1.6819\) | |
| 181944.e1 | 181944bj3 | \([0, 0, 0, -494931, 133846526]\) | \(381775972/567\) | \(19912791644347392\) | \([2]\) | \(1769472\) | \(2.0285\) | |
| 181944.e4 | 181944bj4 | \([0, 0, 0, 154869, 5939894]\) | \(11696828/7203\) | \(-252966204963376128\) | \([2]\) | \(1769472\) | \(2.0285\) |
Rank
sage: E.rank()
The elliptic curves in class 181944bj have rank \(1\).
Complex multiplication
The elliptic curves in class 181944bj do not have complex multiplication.Modular form 181944.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
