Show commands:
SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 194922dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 194922.bm2 | 194922dn1 | \([1, -1, 0, -20036844, 39882913272]\) | \(-24905087205614147556241/4819348696095929736\) | \(-172151954773242706099656\) | \([]\) | \(16708608\) | \(3.1821\) | \(\Gamma_0(N)\)-optimal |
| 194922.bm1 | 194922dn2 | \([1, -1, 0, -789069654, -11414797101324]\) | \(-1521059241134755603512440881/695595284594977727840256\) | \(-24847359161017199416181784576\) | \([]\) | \(116960256\) | \(4.1550\) |
Rank
sage: E.rank()
The elliptic curves in class 194922dn have rank \(1\).
Complex multiplication
The elliptic curves in class 194922dn do not have complex multiplication.Modular form 194922.2.a.dn
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
