Properties

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

Show commands: SageMath
sage: E = EllipticCurve("dq1")

sage: E.isogeny_class()

Elliptic curves in class 115920.dq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.dq1 115920cm1 $$[0, 0, 0, -2427, -39254]$$ $$14295828483/2254000$$ $$249274368000$$ $$$$ $$110592$$ $$0.90963$$ $$\Gamma_0(N)$$-optimal
115920.dq2 115920cm2 $$[0, 0, 0, 4293, -218006]$$ $$79119341757/231437500$$ $$-25595136000000$$ $$$$ $$221184$$ $$1.2562$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 115920.2.a.dq

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} + 4 q^{11} - 6 q^{17} + O(q^{20})$$ 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 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. 