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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 59850.fe
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59850.fe1 | 59850fh6 | \([1, -1, 1, -79990880, 275331257997]\) | \(4969327007303723277361/1123462695162150\) | \(12796942262081364843750\) | \([2]\) | \(11796480\) | \(3.2342\) | |
| 59850.fe2 | 59850fh4 | \([1, -1, 1, -5572130, 3256307997]\) | \(1679731262160129361/570261564022500\) | \(6495635627693789062500\) | \([2, 2]\) | \(5898240\) | \(2.8876\) | |
| 59850.fe3 | 59850fh2 | \([1, -1, 1, -2291630, -1297026003]\) | \(116844823575501841/3760263939600\) | \(42831756437006250000\) | \([2, 2]\) | \(2949120\) | \(2.5411\) | |
| 59850.fe4 | 59850fh1 | \([1, -1, 1, -2273630, -1318986003]\) | \(114113060120923921/124104960\) | \(1413633060000000\) | \([2]\) | \(1474560\) | \(2.1945\) | \(\Gamma_0(N)\)-optimal |
| 59850.fe5 | 59850fh3 | \([1, -1, 1, 700870, -4445136003]\) | \(3342636501165359/751262567039460\) | \(-8557350177683849062500\) | \([2]\) | \(5898240\) | \(2.8876\) | |
| 59850.fe6 | 59850fh5 | \([1, -1, 1, 16358620, 22555367997]\) | \(42502666283088696719/43898058864843750\) | \(-500026326757360839843750\) | \([2]\) | \(11796480\) | \(3.2342\) |
Rank
sage: E.rank()
The elliptic curves in class 59850.fe have rank \(0\).
Complex multiplication
The elliptic curves in class 59850.fe do not have complex multiplication.Modular form 59850.2.a.fe
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
