# Properties

 Label 115920.da Number of curves $4$ Conductor $115920$ CM no Rank $2$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("da1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.da

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.da1 115920ea4 $$[0, 0, 0, -409827, 86681954]$$ $$2549399737314529/388286718750$$ $$1159417929600000000$$ $$[2]$$ $$1572864$$ $$2.1900$$
115920.da2 115920ea2 $$[0, 0, 0, -111747, -13055614]$$ $$51682540549249/5249002500$$ $$15673437480960000$$ $$[2, 2]$$ $$786432$$ $$1.8434$$
115920.da3 115920ea1 $$[0, 0, 0, -108867, -13825726]$$ $$47788676405569/579600$$ $$1730676326400$$ $$[2]$$ $$393216$$ $$1.4969$$ $$\Gamma_0(N)$$-optimal
115920.da4 115920ea3 $$[0, 0, 0, 140253, -63506014]$$ $$102181603702751/642612880350$$ $$-1918831778919014400$$ $$[2]$$ $$1572864$$ $$2.1900$$

## Rank

sage: E.rank()

The elliptic curves in class 115920.da have rank $$2$$.

## Complex multiplication

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

## Modular form 115920.2.a.da

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} - 6 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.