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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 19152.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19152.bj1 | 19152bp3 | \([0, 0, 0, -2613819, 1626526442]\) | \(661397832743623417/443352042\) | \(1323842103779328\) | \([4]\) | \(245760\) | \(2.2178\) | |
| 19152.bj2 | 19152bp2 | \([0, 0, 0, -164379, 25082570]\) | \(164503536215257/4178071044\) | \(12475653288247296\) | \([2, 2]\) | \(122880\) | \(1.8712\) | |
| 19152.bj3 | 19152bp1 | \([0, 0, 0, -23259, -798838]\) | \(466025146777/177366672\) | \(529614044725248\) | \([2]\) | \(61440\) | \(1.5246\) | \(\Gamma_0(N)\)-optimal |
| 19152.bj4 | 19152bp4 | \([0, 0, 0, 27141, 80048810]\) | \(740480746823/927484650666\) | \(-2769454327134265344\) | \([2]\) | \(245760\) | \(2.2178\) |
Rank
sage: E.rank()
The elliptic curves in class 19152.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 19152.bj do not have complex multiplication.Modular form 19152.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
