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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 142296ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142296.j3 | 142296ba1 | \([0, -1, 0, -43479, -3451776]\) | \(2725888/21\) | \(70029919709904\) | \([2]\) | \(552960\) | \(1.4857\) | \(\Gamma_0(N)\)-optimal |
| 142296.j2 | 142296ba2 | \([0, -1, 0, -73124, 1884324]\) | \(810448/441\) | \(23530053022527744\) | \([2, 2]\) | \(1105920\) | \(1.8323\) | |
| 142296.j1 | 142296ba3 | \([0, -1, 0, -903184, 330256060]\) | \(381775972/567\) | \(121011701258714112\) | \([2]\) | \(2211840\) | \(2.1789\) | |
| 142296.j4 | 142296ba4 | \([0, -1, 0, 282616, 14548668]\) | \(11696828/7203\) | \(-1537296797471812608\) | \([2]\) | \(2211840\) | \(2.1789\) |
Rank
sage: E.rank()
The elliptic curves in class 142296ba have rank \(2\).
Complex multiplication
The elliptic curves in class 142296ba do not have complex multiplication.Modular form 142296.2.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.
