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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 200400bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 200400.d3 | 200400bh1 | \([0, -1, 0, -188408, 31539312]\) | \(11556972012529/360720\) | \(23086080000000\) | \([2]\) | \(1050624\) | \(1.6606\) | \(\Gamma_0(N)\)-optimal |
| 200400.d2 | 200400bh2 | \([0, -1, 0, -196408, 28723312]\) | \(13092526729009/2033108100\) | \(130118918400000000\) | \([2, 2]\) | \(2101248\) | \(2.0072\) | |
| 200400.d4 | 200400bh3 | \([0, -1, 0, 343592, 158323312]\) | \(70092508729391/210005006670\) | \(-13440320426880000000\) | \([2]\) | \(4202496\) | \(2.3538\) | |
| 200400.d1 | 200400bh4 | \([0, -1, 0, -864408, -281228688]\) | \(1116093485689489/110938308750\) | \(7100051760000000000\) | \([2]\) | \(4202496\) | \(2.3538\) |
Rank
sage: E.rank()
The elliptic curves in class 200400bh have rank \(0\).
Complex multiplication
The elliptic curves in class 200400bh do not have complex multiplication.Modular form 200400.2.a.bh
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.
