# Properties

 Label 115920.p Number of curves $4$ Conductor $115920$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.p1 115920s4 $$[0, 0, 0, -325083, -66919718]$$ $$5089545532199524/353759765625$$ $$264080250000000000$$ $$$$ $$1179648$$ $$2.0908$$
115920.p2 115920s2 $$[0, 0, 0, -64263, 5014438]$$ $$157267580823376/32806265625$$ $$6122436516000000$$ $$[2, 2]$$ $$589824$$ $$1.7442$$
115920.p3 115920s1 $$[0, 0, 0, -60618, 5744167]$$ $$2111937254864896/132040125$$ $$1540116018000$$ $$$$ $$294912$$ $$1.3976$$ $$\Gamma_0(N)$$-optimal
115920.p4 115920s3 $$[0, 0, 0, 138237, 30245938]$$ $$391353415004156/755885521125$$ $$-564265517977728000$$ $$$$ $$1179648$$ $$2.0908$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.p

sage: E.q_eigenform(10)

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