Properties

 Label 47040.eh Number of curves $2$ Conductor $47040$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("47040.eh1")

sage: E.isogeny_class()

Elliptic curves in class 47040.eh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
47040.eh1 47040cj1 [0, 1, 0, -961, -4705] [2] 36864 $$\Gamma_0(N)$$-optimal
47040.eh2 47040cj2 [0, 1, 0, 3519, -32481] [2] 73728

Rank

sage: E.rank()

The elliptic curves in class 47040.eh have rank $$1$$.

Modular form 47040.2.a.eh

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} - 2q^{11} - 2q^{13} - q^{15} - 4q^{17} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.