# Properties

 Label 13860.c Number of curves $2$ Conductor $13860$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 13860.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.c1 13860a1 $$[0, 0, 0, -34368, 2452333]$$ $$10392086293512192/1684375$$ $$727650000$$ $$$$ $$24960$$ $$1.1024$$ $$\Gamma_0(N)$$-optimal
13860.c2 13860a2 $$[0, 0, 0, -34263, 2468062]$$ $$-643570518871152/8271484375$$ $$-57172500000000$$ $$$$ $$49920$$ $$1.4489$$

## Rank

sage: E.rank()

The elliptic curves in class 13860.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 13860.c do not have complex multiplication.

## Modular form 13860.2.a.c

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} - q^{11} + 6q^{13} - 6q^{17} + O(q^{20})$$ ## 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. 