Properties

 Label 115920.fh Number of curves $2$ Conductor $115920$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("fh1")

sage: E.isogeny_class()

Elliptic curves in class 115920.fh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.fh1 115920ey2 $$[0, 0, 0, -141627, -20514454]$$ $$105214211150329/2028600$$ $$6057367142400$$ $$$$ $$442368$$ $$1.5755$$
115920.fh2 115920ey1 $$[0, 0, 0, -9147, -298006]$$ $$28344726649/3554880$$ $$10614814801920$$ $$$$ $$221184$$ $$1.2289$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 115920.fh have rank $$1$$.

Complex multiplication

The elliptic curves in class 115920.fh do not have complex multiplication.

Modular form 115920.2.a.fh

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} + 6 q^{11} - 2 q^{13} - 6 q^{19} + O(q^{20})$$ 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 