Show commands:
SageMath
E = EllipticCurve("kl1")
E.isogeny_class()
Elliptic curves in class 176400.kl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.kl1 | 176400is2 | \([0, 0, 0, -10087875, -12351858750]\) | \(-30642435/56\) | \(-207485399923200000000\) | \([]\) | \(4976640\) | \(2.7900\) | |
| 176400.kl2 | 176400is1 | \([0, 0, 0, 202125, -82748750]\) | \(179685/686\) | \(-3486551644800000000\) | \([]\) | \(1658880\) | \(2.2407\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.kl have rank \(0\).
Complex multiplication
The elliptic curves in class 176400.kl do not have complex multiplication.Modular form 176400.2.a.kl
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
