Properties

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

Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 15680.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.h1 15680bl1 $$[0, 0, 0, -412972, 102148144]$$ $$-5154200289/20$$ $$-30224159866880$$ $$[]$$ $$161280$$ $$1.7999$$ $$\Gamma_0(N)$$-optimal
15680.h2 15680bl2 $$[0, 0, 0, 2879828, -969197264]$$ $$1747829720511/1280000000$$ $$-1934346231480320000000$$ $$[]$$ $$1128960$$ $$2.7728$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 15680.2.a.h

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 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.