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SageMath
E = EllipticCurve("fj1")
E.isogeny_class()
Elliptic curves in class 203840.fj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203840.fj1 | 203840ci3 | \([0, -1, 0, -650785, -193743423]\) | \(988345570681/44994560\) | \(1387676300591759360\) | \([2]\) | \(3981312\) | \(2.2431\) | |
| 203840.fj2 | 203840ci1 | \([0, -1, 0, -101985, 12495617]\) | \(3803721481/26000\) | \(801865465856000\) | \([2]\) | \(1327104\) | \(1.6938\) | \(\Gamma_0(N)\)-optimal |
| 203840.fj3 | 203840ci2 | \([0, -1, 0, -39265, 27636225]\) | \(-217081801/10562500\) | \(-325757845504000000\) | \([2]\) | \(2654208\) | \(2.0404\) | |
| 203840.fj4 | 203840ci4 | \([0, -1, 0, 352735, -738253375]\) | \(157376536199/7722894400\) | \(-238181627531257446400\) | \([2]\) | \(7962624\) | \(2.5897\) |
Rank
sage: E.rank()
The elliptic curves in class 203840.fj have rank \(1\).
Complex multiplication
The elliptic curves in class 203840.fj do not have complex multiplication.Modular form 203840.2.a.fj
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
