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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 138720.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 138720.ba1 | 138720bh4 | \([0, 1, 0, -46336, -3854500]\) | \(890277128/15\) | \(185376529920\) | \([2]\) | \(294912\) | \(1.2924\) | |
| 138720.ba2 | 138720bh2 | \([0, 1, 0, -11656, 421544]\) | \(14172488/1875\) | \(23172066240000\) | \([2]\) | \(294912\) | \(1.2924\) | |
| 138720.ba3 | 138720bh1 | \([0, 1, 0, -2986, -57040]\) | \(1906624/225\) | \(347580993600\) | \([2, 2]\) | \(147456\) | \(0.94584\) | \(\Gamma_0(N)\)-optimal |
| 138720.ba4 | 138720bh3 | \([0, 1, 0, 4239, -283905]\) | \(85184/405\) | \(-40041330462720\) | \([2]\) | \(294912\) | \(1.2924\) |
Rank
sage: E.rank()
The elliptic curves in class 138720.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 138720.ba do not have complex multiplication.Modular form 138720.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
