# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("ct1")

sage: E.isogeny_class()

## Elliptic curves in class 115920ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.r2 115920ct1 $$[0, 0, 0, -232203, 43066298]$$ $$463702796512201/15214500$$ $$45430253568000$$ $$$$ $$552960$$ $$1.7143$$ $$\Gamma_0(N)$$-optimal
115920.r3 115920ct2 $$[0, 0, 0, -222123, 46975322]$$ $$-405897921250921/84358968750$$ $$-251894530944000000$$ $$$$ $$1105920$$ $$2.0609$$
115920.r1 115920ct3 $$[0, 0, 0, -415803, -33939862]$$ $$2662558086295801/1374177967680$$ $$4103273424644997120$$ $$$$ $$1658880$$ $$2.2636$$
115920.r4 115920ct4 $$[0, 0, 0, 1559877, -263513878]$$ $$140574743422291079/91397357868600$$ $$-272911048237913702400$$ $$$$ $$3317760$$ $$2.6102$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.ct

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 