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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 7744.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7744.x1 | 7744f3 | \([0, 1, 0, -3785041, 2833092073]\) | \(-52893159101157376/11\) | \(-1247178944\) | \([]\) | \(48000\) | \(2.0422\) | |
| 7744.x2 | 7744f2 | \([0, 1, 0, -5001, 244913]\) | \(-122023936/161051\) | \(-18259946919104\) | \([]\) | \(9600\) | \(1.2375\) | |
| 7744.x3 | 7744f1 | \([0, 1, 0, -161, -1927]\) | \(-4096/11\) | \(-1247178944\) | \([]\) | \(1920\) | \(0.43279\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7744.x have rank \(0\).
Complex multiplication
The elliptic curves in class 7744.x do not have complex multiplication.Modular form 7744.2.a.x
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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
