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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 23232dq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23232.dr4 | 23232dq1 | \([0, 1, 0, 323, 61235]\) | \(2048/891\) | \(-1616343911424\) | \([2]\) | \(46080\) | \(1.0217\) | \(\Gamma_0(N)\)-optimal |
| 23232.dr3 | 23232dq2 | \([0, 1, 0, -21457, 1172015]\) | \(37642192/1089\) | \(31608503156736\) | \([2, 2]\) | \(92160\) | \(1.3683\) | |
| 23232.dr2 | 23232dq3 | \([0, 1, 0, -50497, -2713537]\) | \(122657188/43923\) | \(5099505175953408\) | \([2]\) | \(184320\) | \(1.7148\) | |
| 23232.dr1 | 23232dq4 | \([0, 1, 0, -340897, 76495967]\) | \(37736227588/33\) | \(3831333715968\) | \([2]\) | \(184320\) | \(1.7148\) |
Rank
sage: E.rank()
The elliptic curves in class 23232dq have rank \(0\).
Complex multiplication
The elliptic curves in class 23232dq do not have complex multiplication.Modular form 23232.2.a.dq
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.
