Properties

 Label 4032h Number of curves 6 Conductor 4032 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4032.h1")
sage: E.isogeny_class()

Elliptic curves in class 4032h

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
4032.h6 4032h1 [0, 0, 0, 564, 1136] 2 2048 $$\Gamma_0(N)$$-optimal
4032.h5 4032h2 [0, 0, 0, -2316, 9200] 4 4096
4032.h3 4032h3 [0, 0, 0, -22476, -1289104] 2 8192
4032.h2 4032h4 [0, 0, 0, -28236, 1823600] 4 8192
4032.h1 4032h5 [0, 0, 0, -451596, 116808176] 2 16384
4032.h4 4032h6 [0, 0, 0, -19596, 2960624] 2 16384

Rank

sage: E.rank()

The elliptic curves in class 4032h have rank $$0$$.

Modular form4032.2.a.h

sage: E.q_eigenform(10)
$$q - 2q^{5} - q^{7} + 4q^{11} + 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.