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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 7938.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7938.x1 | 7938u4 | \([1, -1, 1, -475040, 126139843]\) | \(-189613868625/128\) | \(-8003008282752\) | \([]\) | \(45360\) | \(1.7916\) | |
| 7938.x2 | 7938u3 | \([1, -1, 1, -4640, 248259]\) | \(-1159088625/2097152\) | \(-19984954687488\) | \([]\) | \(15120\) | \(1.2423\) | |
| 7938.x3 | 7938u1 | \([1, -1, 1, -230, -1347]\) | \(-140625/8\) | \(-76236552\) | \([]\) | \(2160\) | \(0.26937\) | \(\Gamma_0(N)\)-optimal |
| 7938.x4 | 7938u2 | \([1, -1, 1, 1240, -2915]\) | \(3375/2\) | \(-125047004418\) | \([]\) | \(6480\) | \(0.81867\) |
Rank
sage: E.rank()
The elliptic curves in class 7938.x have rank \(1\).
Complex multiplication
The elliptic curves in class 7938.x do not have complex multiplication.Modular form 7938.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
