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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 141120ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.lv4 | 141120ba1 | \([0, 0, 0, 15288, 6006616]\) | \(4499456/180075\) | \(-15814998260812800\) | \([2]\) | \(786432\) | \(1.7882\) | \(\Gamma_0(N)\)-optimal |
| 141120.lv3 | 141120ba2 | \([0, 0, 0, -416892, 99184624]\) | \(5702413264/275625\) | \(387306079856640000\) | \([2, 2]\) | \(1572864\) | \(2.1347\) | |
| 141120.lv1 | 141120ba3 | \([0, 0, 0, -6590892, 6512735824]\) | \(5633270409316/14175\) | \(79674393570508800\) | \([2]\) | \(3145728\) | \(2.4813\) | |
| 141120.lv2 | 141120ba4 | \([0, 0, 0, -1157772, -350974064]\) | \(30534944836/8203125\) | \(46107866649600000000\) | \([2]\) | \(3145728\) | \(2.4813\) |
Rank
sage: E.rank()
The elliptic curves in class 141120ba have rank \(1\).
Complex multiplication
The elliptic curves in class 141120ba do not have complex multiplication.Modular form 141120.2.a.ba
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.
