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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 84150.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84150.ba1 | 84150ct2 | \([1, -1, 0, -1342197, 598892341]\) | \(-14672534807538428665/1281210974208\) | \(-23350070004940800\) | \([]\) | \(1741824\) | \(2.1822\) | |
| 84150.ba2 | 84150ct1 | \([1, -1, 0, 378, 2396596]\) | \(327254135/136157231232\) | \(-2481465539203200\) | \([]\) | \(580608\) | \(1.6329\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 84150.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 84150.ba do not have complex multiplication.Modular form 84150.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
