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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 40425.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40425.y1 | 40425ck4 | \([1, 0, 0, -704396463, -7195772152458]\) | \(21026497979043461623321/161783881875\) | \(297401748729873046875\) | \([2]\) | \(8847360\) | \(3.5210\) | |
| 40425.y2 | 40425ck2 | \([1, 0, 0, -44054088, -112279495833]\) | \(5143681768032498601/14238434358225\) | \(26174024434543953515625\) | \([2, 2]\) | \(4423680\) | \(3.1744\) | |
| 40425.y3 | 40425ck3 | \([1, 0, 0, -26689713, -201688662708]\) | \(-1143792273008057401/8897444448004035\) | \(-16355866279112917401796875\) | \([2]\) | \(8847360\) | \(3.5210\) | |
| 40425.y4 | 40425ck1 | \([1, 0, 0, -3867963, -200393208]\) | \(3481467828171481/2005331497785\) | \(3686331959107929140625\) | \([4]\) | \(2211840\) | \(2.8278\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40425.y have rank \(1\).
Complex multiplication
The elliptic curves in class 40425.y do not have complex multiplication.Modular form 40425.2.a.y
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
