# Properties

 Label 115920.cc Number of curves $2$ Conductor $115920$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cc1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.cc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.cc1 115920g2 $$[0, 0, 0, -310203, 66480202]$$ $$59699126465470854/19845765625$$ $$1097391456000000$$ $$$$ $$638976$$ $$1.8589$$
115920.cc2 115920g1 $$[0, 0, 0, -22083, 731218]$$ $$43075884983148/16573802875$$ $$458232501888000$$ $$$$ $$319488$$ $$1.5123$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.cc

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} + 4 q^{11} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 