Properties

 Label 338.e Number of curves $2$ Conductor $338$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
E = EllipticCurve("e1")

E.isogeny_class()

Elliptic curves in class 338.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
338.e1 338b2 $$[1, -1, 1, -65773, -6478507]$$ $$-38575685889/16384$$ $$-13364932132864$$ $$[]$$ $$1092$$ $$1.4794$$
338.e2 338b1 $$[1, -1, 1, 137, 2643]$$ $$351/4$$ $$-3262922884$$ $$[]$$ $$156$$ $$0.50645$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 338.e have rank $$0$$.

Complex multiplication

The elliptic curves in class 338.e do not have complex multiplication.

Modular form338.2.a.e

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + 4 q^{7} + q^{8} - 3 q^{9} - q^{10} + 4 q^{11} + 4 q^{14} + q^{16} + 3 q^{17} - 3 q^{18} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.