Properties

 Label 51.a Number of curves 2 Conductor 51 CM no Rank 0 Graph Related objects

Show commands for: SageMath
sage: E = EllipticCurve("51.a1")
sage: E.isogeny_class()

Elliptic curves in class 51.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
51.a1 51a2 [0, 1, 1, -59, -196] 1 6
51.a2 51a1 [0, 1, 1, 1, -1] 3 2 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 51.a have rank $$0$$.

Modular form51.2.a.a

sage: E.q_eigenform(10)
$$q + q^{3} - 2q^{4} + 3q^{5} - 4q^{7} + q^{9} - 3q^{11} - 2q^{12} - q^{13} + 3q^{15} + 4q^{16} - q^{17} - q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels. 