Show commands:
SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 154800di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154800.fy3 | 154800di1 | \([0, 0, 0, -246675, -47096750]\) | \(35578826569/51600\) | \(2407449600000000\) | \([2]\) | \(884736\) | \(1.8535\) | \(\Gamma_0(N)\)-optimal |
| 154800.fy2 | 154800di2 | \([0, 0, 0, -318675, -17360750]\) | \(76711450249/41602500\) | \(1941006240000000000\) | \([2, 2]\) | \(1769472\) | \(2.2001\) | |
| 154800.fy1 | 154800di3 | \([0, 0, 0, -3018675, 2004939250]\) | \(65202655558249/512820150\) | \(23926136918400000000\) | \([2]\) | \(3538944\) | \(2.5467\) | |
| 154800.fy4 | 154800di4 | \([0, 0, 0, 1229325, -136556750]\) | \(4403686064471/2721093750\) | \(-126955350000000000000\) | \([2]\) | \(3538944\) | \(2.5467\) |
Rank
sage: E.rank()
The elliptic curves in class 154800di have rank \(1\).
Complex multiplication
The elliptic curves in class 154800di do not have complex multiplication.Modular form 154800.2.a.di
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.
