Properties

 Label 115920.dk Number of curves $2$ Conductor $115920$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("dk1")

sage: E.isogeny_class()

Elliptic curves in class 115920.dk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.dk1 115920ek1 $$[0, 0, 0, -16169187, 25025360866]$$ $$156567200830221067489/16905000000$$ $$50478059520000000$$ $$[2]$$ $$3354624$$ $$2.6319$$ $$\Gamma_0(N)$$-optimal
115920.dk2 115920ek2 $$[0, 0, 0, -16128867, 25156376674]$$ $$-155398856216042825569/1627294921875000$$ $$-4859076600000000000000$$ $$[2]$$ $$6709248$$ $$2.9785$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 115920.2.a.dk

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} + 6 q^{13} - 4 q^{17} - 4 q^{19} + O(q^{20})$$

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.