# Properties

 Label 115920.ca Number of curves $2$ Conductor $115920$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ca1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ca1 115920di1 $$[0, 0, 0, -17191803, 27435410602]$$ $$188191720927962271801/9422571110400$$ $$28135646574516633600$$ $$[2]$$ $$5308416$$ $$2.8029$$ $$\Gamma_0(N)$$-optimal
115920.ca2 115920di2 $$[0, 0, 0, -16270203, 30507472042]$$ $$-159520003524722950201/42335913815758080$$ $$-126414361279232574750720$$ $$[2]$$ $$10616832$$ $$3.1494$$

## Rank

sage: E.rank()

The elliptic curves in class 115920.ca have rank $$0$$.

## Complex multiplication

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

## Modular form 115920.2.a.ca

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} + 2 q^{11} + 4 q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.