Show commands:
SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 369600dt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.dt3 | 369600dt1 | \([0, -1, 0, -325633, 71579137]\) | \(932288503609/779625\) | \(3193344000000000\) | \([2]\) | \(3538944\) | \(1.9029\) | \(\Gamma_0(N)\)-optimal |
| 369600.dt2 | 369600dt2 | \([0, -1, 0, -397633, 37667137]\) | \(1697509118089/833765625\) | \(3415104000000000000\) | \([2, 2]\) | \(7077888\) | \(2.2495\) | |
| 369600.dt4 | 369600dt3 | \([0, -1, 0, 1450367, 287147137]\) | \(82375335041831/56396484375\) | \(-231000000000000000000\) | \([2]\) | \(14155776\) | \(2.5960\) | |
| 369600.dt1 | 369600dt4 | \([0, -1, 0, -3397633, -2383332863]\) | \(1058993490188089/13182390375\) | \(53995070976000000000\) | \([2]\) | \(14155776\) | \(2.5960\) |
Rank
sage: E.rank()
The elliptic curves in class 369600dt have rank \(0\).
Complex multiplication
The elliptic curves in class 369600dt do not have complex multiplication.Modular form 369600.2.a.dt
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
