Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 4400.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4400.r1 | 4400c3 | \([0, 0, 0, -188675, 1623250]\) | \(46424454082884/26794860125\) | \(428717762000000000\) | \([4]\) | \(55296\) | \(2.0728\) | |
| 4400.r2 | 4400c2 | \([0, 0, 0, -126175, -17189250]\) | \(55537159171536/228765625\) | \(915062500000000\) | \([2, 2]\) | \(27648\) | \(1.7263\) | |
| 4400.r3 | 4400c1 | \([0, 0, 0, -126050, -17225125]\) | \(885956203616256/15125\) | \(3781250000\) | \([2]\) | \(13824\) | \(1.3797\) | \(\Gamma_0(N)\)-optimal |
| 4400.r4 | 4400c4 | \([0, 0, 0, -65675, -33705750]\) | \(-1957960715364/29541015625\) | \(-472656250000000000\) | \([2]\) | \(55296\) | \(2.0728\) |
Rank
sage: E.rank()
The elliptic curves in class 4400.r have rank \(0\).
Complex multiplication
The elliptic curves in class 4400.r do not have complex multiplication.Modular form 4400.2.a.r
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 LMFDB 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 LMFDB labels.
