# Properties

 Label 13860.g Number of curves $2$ Conductor $13860$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 13860.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.g1 13860b2 $$[0, 0, 0, -8343, 210222]$$ $$12745567728/3587045$$ $$18074574524160$$ $$$$ $$32256$$ $$1.2508$$
13860.g2 13860b1 $$[0, 0, 0, -7668, 258417]$$ $$158328373248/21175$$ $$6668600400$$ $$$$ $$16128$$ $$0.90419$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 13860.g have rank $$1$$.

## Complex multiplication

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

## Modular form 13860.2.a.g

sage: E.q_eigenform(10)

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