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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 76608dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76608.cy3 | 76608dg1 | \([0, 0, 0, -1082220, 308857936]\) | \(19804628171203875/5638671302656\) | \(39909883949013270528\) | \([2]\) | \(1769472\) | \(2.4678\) | \(\Gamma_0(N)\)-optimal |
| 76608.cy4 | 76608dg2 | \([0, 0, 0, 2849940, 2037435472]\) | \(361682234074684125/462672528510976\) | \(-3274744337477494898688\) | \([2]\) | \(3538944\) | \(2.8143\) | |
| 76608.cy1 | 76608dg3 | \([0, 0, 0, -80462700, 277804960848]\) | \(11165451838341046875/572244736\) | \(2952657145348227072\) | \([2]\) | \(5308416\) | \(3.0171\) | |
| 76608.cy2 | 76608dg4 | \([0, 0, 0, -80324460, 278807090256]\) | \(-11108001800138902875/79947274872976\) | \(-412510378085524860567552\) | \([2]\) | \(10616832\) | \(3.3636\) |
Rank
sage: E.rank()
The elliptic curves in class 76608dg have rank \(1\).
Complex multiplication
The elliptic curves in class 76608dg do not have complex multiplication.Modular form 76608.2.a.dg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
