Properties

 Label 15680bl Number of curves $2$ Conductor $15680$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bl1")

sage: E.isogeny_class()

Elliptic curves in class 15680bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.h1 15680bl1 [0, 0, 0, -412972, 102148144] [] 161280 $$\Gamma_0(N)$$-optimal
15680.h2 15680bl2 [0, 0, 0, 2879828, -969197264] [] 1128960

Rank

sage: E.rank()

The elliptic curves in class 15680bl have rank $$0$$.

Complex multiplication

The elliptic curves in class 15680bl do not have complex multiplication.

Modular form 15680.2.a.bl

sage: E.q_eigenform(10)

$$q - 3q^{3} + q^{5} + 6q^{9} + 2q^{11} - 3q^{15} - 4q^{17} + 6q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.