# Properties

 Label 377520.dy Number of curves $4$ Conductor $377520$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("dy1")

sage: E.isogeny_class()

## Elliptic curves in class 377520.dy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
377520.dy1 377520dy3 $$[0, 1, 0, -3104963616, 66592625380884]$$ $$912446049969377120252018/17177299425$$ $$62321937913144166400$$ $$$$ $$165150720$$ $$3.7863$$
377520.dy2 377520dy4 $$[0, 1, 0, -211369616, 843820298484]$$ $$287849398425814280018/81784533026485575$$ $$296727120103288446428313600$$ $$$$ $$165150720$$ $$3.7863$$
377520.dy3 377520dy2 $$[0, 1, 0, -194066616, 1040389299684]$$ $$445574312599094932036/61129333175625$$ $$110893406832582042240000$$ $$[2, 2]$$ $$82575360$$ $$3.4397$$
377520.dy4 377520dy1 $$[0, 1, 0, -11054116, 19252754684]$$ $$-329381898333928144/162600887109375$$ $$-73742691883103100000000$$ $$$$ $$41287680$$ $$3.0931$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 377520.dy have rank $$1$$.

## Complex multiplication

The elliptic curves in class 377520.dy do not have complex multiplication.

## Modular form 377520.2.a.dy

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - 4 q^{7} + q^{9} - q^{13} - q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 