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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 25350bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25350.bt4 | 25350bg1 | \([1, 0, 1, -82476, 190325098]\) | \(-822656953/207028224\) | \(-15613838982144000000\) | \([2]\) | \(860160\) | \(2.3621\) | \(\Gamma_0(N)\)-optimal |
| 25350.bt3 | 25350bg2 | \([1, 0, 1, -5490476, 4906101098]\) | \(242702053576633/2554695936\) | \(192672333377316000000\) | \([2, 2]\) | \(1720320\) | \(2.7087\) | |
| 25350.bt2 | 25350bg3 | \([1, 0, 1, -9884476, -4057658902]\) | \(1416134368422073/725251155408\) | \(54697637565370829250000\) | \([2]\) | \(3440640\) | \(3.0553\) | |
| 25350.bt1 | 25350bg4 | \([1, 0, 1, -87624476, 315701157098]\) | \(986551739719628473/111045168\) | \(8374903379826750000\) | \([2]\) | \(3440640\) | \(3.0553\) |
Rank
sage: E.rank()
The elliptic curves in class 25350bg have rank \(0\).
Complex multiplication
The elliptic curves in class 25350bg do not have complex multiplication.Modular form 25350.2.a.bg
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 Cremona 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 Cremona labels.
