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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1813.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1813.b1 | 1813c3 | \([0, -1, 1, -91793, 10735059]\) | \(727057727488000/37\) | \(4353013\) | \([]\) | \(2268\) | \(1.1950\) | |
| 1813.b2 | 1813c2 | \([0, -1, 1, -1143, 14790]\) | \(1404928000/50653\) | \(5959274797\) | \([]\) | \(756\) | \(0.64573\) | |
| 1813.b3 | 1813c1 | \([0, -1, 1, -163, -743]\) | \(4096000/37\) | \(4353013\) | \([]\) | \(252\) | \(0.096424\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1813.b have rank \(1\).
Complex multiplication
The elliptic curves in class 1813.b do not have complex multiplication.Modular form 1813.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
