Properties

 Label 9408.bh Number of curves 2 Conductor 9408 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.bh1")

sage: E.isogeny_class()

Elliptic curves in class 9408.bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.bh1 9408j2 [0, -1, 0, -1017, 12825] [2] 3072
9408.bh2 9408j1 [0, -1, 0, -72, 162] [2] 1536 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 9408.bh have rank $$0$$.

Modular form9408.2.a.bh

sage: E.q_eigenform(10)

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

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.