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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 2304.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2304.b1 | 2304o3 | \([0, 0, 0, -5826, -171160]\) | \(58591911104/243\) | \(90699264\) | \([2]\) | \(1280\) | \(0.73631\) | |
| 2304.b2 | 2304o4 | \([0, 0, 0, -5736, -176704]\) | \(-873722816/59049\) | \(-1410554953728\) | \([2]\) | \(2560\) | \(1.0829\) | |
| 2304.b3 | 2304o1 | \([0, 0, 0, -66, 200]\) | \(85184/3\) | \(1119744\) | \([2]\) | \(256\) | \(-0.068409\) | \(\Gamma_0(N)\)-optimal |
| 2304.b4 | 2304o2 | \([0, 0, 0, 24, 704]\) | \(64/9\) | \(-214990848\) | \([2]\) | \(512\) | \(0.27816\) |
Rank
sage: E.rank()
The elliptic curves in class 2304.b have rank \(1\).
Complex multiplication
The elliptic curves in class 2304.b do not have complex multiplication.Modular form 2304.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
