Properties

 Label 1342.b Number of curves 3 Conductor 1342 CM no Rank 0 Graph Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1342.b1")
sage: E.isogeny_class()

Elliptic curves in class 1342.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1342.b1 1342c3 [1, 1, 1, -117257250, -488766109679] 1 80000
1342.b2 1342c2 [1, 1, 1, -187880, -31262199] 5 16000
1342.b3 1342c1 [1, 1, 1, -13960, 629001] 5 3200 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 1342.b have rank $$0$$.

Modular form1342.2.a.b

sage: E.q_eigenform(10)
$$q + q^{2} - q^{3} + q^{4} - 4q^{5} - q^{6} - 2q^{7} + q^{8} - 2q^{9} - 4q^{10} + q^{11} - q^{12} - q^{13} - 2q^{14} + 4q^{15} + q^{16} + 3q^{17} - 2q^{18} + O(q^{20})$$

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.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels. 