Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 25536.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25536.m1 | 25536ch4 | \([0, -1, 0, -12929, 473889]\) | \(1823652903746/328593657\) | \(43069427810304\) | \([4]\) | \(81920\) | \(1.3352\) | |
| 25536.m2 | 25536ch2 | \([0, -1, 0, -3809, -82431]\) | \(93280467172/7800849\) | \(511236440064\) | \([2, 2]\) | \(40960\) | \(0.98860\) | |
| 25536.m3 | 25536ch1 | \([0, -1, 0, -3729, -86415]\) | \(350104249168/2793\) | \(45760512\) | \([2]\) | \(20480\) | \(0.64202\) | \(\Gamma_0(N)\)-optimal |
| 25536.m4 | 25536ch3 | \([0, -1, 0, 4031, -385055]\) | \(55251546334/517244049\) | \(-67796211990528\) | \([2]\) | \(81920\) | \(1.3352\) |
Rank
sage: E.rank()
The elliptic curves in class 25536.m have rank \(1\).
Complex multiplication
The elliptic curves in class 25536.m do not have complex multiplication.Modular form 25536.2.a.m
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.
