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SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 346800.fm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346800.fm1 | 346800fm4 | \([0, -1, 0, -194875419008, -33111800741923488]\) | \(1059623036730633329075378/154307373046875\) | \(119187355652085937500000000000\) | \([2]\) | \(1486356480\) | \(4.9877\) | |
| 346800.fm2 | 346800fm3 | \([0, -1, 0, -22655117008, 495005063996512]\) | \(1664865424893526702418/826424127435466125\) | \(638331820775627412459204000000000\) | \([2]\) | \(1486356480\) | \(4.9877\) | |
| 346800.fm3 | 346800fm2 | \([0, -1, 0, -12214992008, -514220939503488]\) | \(521902963282042184836/6241849278890625\) | \(2410609082509163270250000000000\) | \([2, 2]\) | \(743178240\) | \(4.6411\) | |
| 346800.fm4 | 346800fm1 | \([0, -1, 0, -146207508, -20655928591488]\) | \(-3579968623693264/1906997690433375\) | \(-184121153342704915861500000000\) | \([2]\) | \(371589120\) | \(4.2945\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346800.fm have rank \(1\).
Complex multiplication
The elliptic curves in class 346800.fm do not have complex multiplication.Modular form 346800.2.a.fm
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.
