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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 10192.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10192.bg1 | 10192u3 | \([0, 1, 0, -360264, -83350156]\) | \(-10730978619193/6656\) | \(-3207461863424\) | \([]\) | \(54432\) | \(1.7205\) | |
| 10192.bg2 | 10192u2 | \([0, 1, 0, -3544, -163052]\) | \(-10218313/17576\) | \(-8469703983104\) | \([]\) | \(18144\) | \(1.1712\) | |
| 10192.bg3 | 10192u1 | \([0, 1, 0, 376, 4724]\) | \(12167/26\) | \(-12529147904\) | \([]\) | \(6048\) | \(0.62188\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10192.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 10192.bg do not have complex multiplication.Modular form 10192.2.a.bg
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.
