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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 116688.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116688.x1 | 116688w1 | \([0, 1, 0, -6703066448, -45095778953004]\) | \(8131755985964161964448308988625/4491414222168968491132426977\) | \(18396832654004094939678420897792\) | \([2]\) | \(189235200\) | \(4.6897\) | \(\Gamma_0(N)\)-optimal |
| 116688.x2 | 116688w2 | \([0, 1, 0, 26124027392, -356388544418956]\) | \(481375691534989591168533139109375/291970430882721534414299079537\) | \(-1195910884895627404960969029783552\) | \([2]\) | \(378470400\) | \(5.0362\) |
Rank
sage: E.rank()
The elliptic curves in class 116688.x have rank \(0\).
Complex multiplication
The elliptic curves in class 116688.x do not have complex multiplication.Modular form 116688.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
