# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.s1 115920r4 $$[0, 0, 0, -1199523, 505601602]$$ $$127847420666360642/17899707105$$ $$26724119510108160$$ $$$$ $$1572864$$ $$2.1688$$
115920.s2 115920r3 $$[0, 0, 0, -487443, -125953742]$$ $$8579021289461282/374333754375$$ $$558877300611840000$$ $$$$ $$1572864$$ $$2.1688$$
115920.s3 115920r2 $$[0, 0, 0, -81723, 6392122]$$ $$80859142234084/23148101025$$ $$17279964822758400$$ $$[2, 2]$$ $$786432$$ $$1.8222$$
115920.s4 115920r1 $$[0, 0, 0, 13497, 659878]$$ $$1457028215984/1851148215$$ $$-345468684476160$$ $$$$ $$393216$$ $$1.4756$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.s

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 