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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 798.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 798.b1 | 798c1 | \([1, 0, 1, -92, 326]\) | \(84778086457/904932\) | \(904932\) | \([2]\) | \(160\) | \(-0.041186\) | \(\Gamma_0(N)\)-optimal |
| 798.b2 | 798c2 | \([1, 0, 1, -22, 830]\) | \(-1102302937/298433646\) | \(-298433646\) | \([2]\) | \(320\) | \(0.30539\) |
Rank
sage: E.rank()
The elliptic curves in class 798.b have rank \(1\).
Complex multiplication
The elliptic curves in class 798.b do not have complex multiplication.Modular form 798.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
