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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 380926bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 380926.bg2 | 380926bg1 | \([1, 0, 0, -36254, 2660020]\) | \(-3183010111/8464\) | \(-14012960201968\) | \([2]\) | \(1204224\) | \(1.3973\) | \(\Gamma_0(N)\)-optimal |
| 380926.bg1 | 380926bg2 | \([1, 0, 0, -580434, 170158624]\) | \(13062552753151/92\) | \(152314784804\) | \([2]\) | \(2408448\) | \(1.7439\) |
Rank
sage: E.rank()
The elliptic curves in class 380926bg have rank \(2\).
Complex multiplication
The elliptic curves in class 380926bg do not have complex multiplication.Modular form 380926.2.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 Cremona 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 Cremona labels.
