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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 25536t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25536.bq3 | 25536t1 | \([0, -1, 0, -10337, -233247]\) | \(466025146777/177366672\) | \(46495608864768\) | \([2]\) | \(61440\) | \(1.3219\) | \(\Gamma_0(N)\)-optimal |
| 25536.bq2 | 25536t2 | \([0, -1, 0, -73057, 7456225]\) | \(164503536215257/4178071044\) | \(1095256255758336\) | \([2, 2]\) | \(122880\) | \(1.6684\) | |
| 25536.bq4 | 25536t3 | \([0, -1, 0, 12063, 23714145]\) | \(740480746823/927484650666\) | \(-243134536264187904\) | \([2]\) | \(245760\) | \(2.0150\) | |
| 25536.bq1 | 25536t4 | \([0, -1, 0, -1161697, 482320993]\) | \(661397832743623417/443352042\) | \(116222077698048\) | \([2]\) | \(245760\) | \(2.0150\) |
Rank
sage: E.rank()
The elliptic curves in class 25536t have rank \(1\).
Complex multiplication
The elliptic curves in class 25536t do not have complex multiplication.Modular form 25536.2.a.t
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.
