Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 254320.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254320.l1 | 254320l1 | \([0, -1, 0, -11281797136, -461751936729664]\) | \(-1606220241149825308027441/2128704136908800000\) | \(-210459619267467701072691200000\) | \([]\) | \(331776000\) | \(4.5329\) | \(\Gamma_0(N)\)-optimal |
| 254320.l2 | 254320l2 | \([0, -1, 0, 79919204464, 5392030330357696]\) | \(570983676137286216962798159/457469996554140806256680\) | \(-45228906935317856037831660383928320\) | \([]\) | \(1658880000\) | \(5.3376\) |
Rank
sage: E.rank()
The elliptic curves in class 254320.l have rank \(1\).
Complex multiplication
The elliptic curves in class 254320.l do not have complex multiplication.Modular form 254320.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
