# Properties

 Label 115920.dr Number of curves $4$ Conductor $115920$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("dr1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.dr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.dr1 115920en4 $$[0, 0, 0, -6624147, 6562103186]$$ $$10765299591712341649/20708625$$ $$61835622912000$$ $$[2]$$ $$2162688$$ $$2.3279$$
115920.dr2 115920en2 $$[0, 0, 0, -414147, 102461186]$$ $$2630872462131649/3645140625$$ $$10884331584000000$$ $$[2, 2]$$ $$1081344$$ $$1.9814$$
115920.dr3 115920en3 $$[0, 0, 0, -298227, 161047154]$$ $$-982374577874929/3183837890625$$ $$-9506889000000000000$$ $$[2]$$ $$2162688$$ $$2.3279$$
115920.dr4 115920en1 $$[0, 0, 0, -33267, 613874]$$ $$1363569097969/734582625$$ $$2193451964928000$$ $$[2]$$ $$540672$$ $$1.6348$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.dr

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} + 4q^{11} + 2q^{13} + 2q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.