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SageMath
E = EllipticCurve("im1")
E.isogeny_class()
Elliptic curves in class 388080.im
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.im1 | 388080im4 | \([0, 0, 0, -1877689947, -31317272788214]\) | \(2084105208962185000201/31185000\) | \(10955229115944960000\) | \([2]\) | \(113246208\) | \(3.6569\) | |
| 388080.im2 | 388080im3 | \([0, 0, 0, -127237467, -402077922806]\) | \(648474704552553481/176469171805080\) | \(61993272696030329629409280\) | \([2]\) | \(113246208\) | \(3.6569\) | |
| 388080.im3 | 388080im2 | \([0, 0, 0, -117359067, -489302219126]\) | \(508859562767519881/62240270400\) | \(21864884478767588966400\) | \([2, 2]\) | \(56623104\) | \(3.3104\) | |
| 388080.im4 | 388080im1 | \([0, 0, 0, -6720987, -8978058614]\) | \(-95575628340361/43812679680\) | \(-15391308131406320762880\) | \([2]\) | \(28311552\) | \(2.9638\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388080.im have rank \(1\).
Complex multiplication
The elliptic curves in class 388080.im do not have complex multiplication.Modular form 388080.2.a.im
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
