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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 2790.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2790.b1 | 2790a2 | \([1, -1, 0, -2283810, -1327854700]\) | \(66928707375050045043/155000000000\) | \(3050865000000000\) | \([2]\) | \(51840\) | \(2.2143\) | |
| 2790.b2 | 2790a1 | \([1, -1, 0, -141090, -21224044]\) | \(-15780576012359283/787251200000\) | \(-15495465369600000\) | \([2]\) | \(25920\) | \(1.8677\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2790.b have rank \(1\).
Complex multiplication
The elliptic curves in class 2790.b do not have complex multiplication.Modular form 2790.2.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.
