Properties

 Label 152880hv Number of curves $4$ Conductor $152880$ CM no Rank $2$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("hv1")

sage: E.isogeny_class()

Elliptic curves in class 152880hv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
152880.e4 152880hv1 $$[0, -1, 0, -996, 43296]$$ $$-3631696/24375$$ $$-734129760000$$ $$[2]$$ $$221184$$ $$0.96019$$ $$\Gamma_0(N)$$-optimal
152880.e3 152880hv2 $$[0, -1, 0, -25496, 1572096]$$ $$15214885924/38025$$ $$4580969702400$$ $$[2, 2]$$ $$442368$$ $$1.3068$$
152880.e1 152880hv3 $$[0, -1, 0, -407696, 100332576]$$ $$31103978031362/195$$ $$46984304640$$ $$[2]$$ $$884736$$ $$1.6533$$
152880.e2 152880hv4 $$[0, -1, 0, -35296, 262816]$$ $$20183398562/11567205$$ $$2787061966940160$$ $$[2]$$ $$884736$$ $$1.6533$$

Rank

sage: E.rank()

The elliptic curves in class 152880hv have rank $$2$$.

Complex multiplication

The elliptic curves in class 152880hv do not have complex multiplication.

Modular form 152880.2.a.hv

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} - 4q^{11} - q^{13} + q^{15} - 6q^{17} + O(q^{20})$$

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.