Properties

 Label 277200.kh Number of curves 4 Conductor 277200 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("277200.kh1")

sage: E.isogeny_class()

Elliptic curves in class 277200.kh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
277200.kh1 277200kh4 [0, 0, 0, -94017675, -340940375750] [2] 47775744
277200.kh2 277200kh2 [0, 0, 0, -12873675, 17620848250] [2] 15925248
277200.kh3 277200kh1 [0, 0, 0, -201675, 678384250] [2] 7962624 $$\Gamma_0(N)$$-optimal
277200.kh4 277200kh3 [0, 0, 0, 1814325, -18274031750] [2] 23887872

Rank

sage: E.rank()

The elliptic curves in class 277200.kh have rank $$0$$.

Modular form 277200.2.a.kh

sage: E.q_eigenform(10)

$$q + q^{7} - q^{11} + 4q^{13} + 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.