# Properties

 Label 130.c Number of curves $2$ Conductor $130$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 130.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
130.c1 130c1 $$[1, 1, 1, -841, -9737]$$ $$65787589563409/10400000$$ $$10400000$$ $$$$ $$80$$ $$0.35695$$ $$\Gamma_0(N)$$-optimal
130.c2 130c2 $$[1, 1, 1, -761, -11561]$$ $$-48743122863889/26406250000$$ $$-26406250000$$ $$$$ $$160$$ $$0.70352$$

## Rank

sage: E.rank()

The elliptic curves in class 130.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 130.c do not have complex multiplication.

## Modular form130.2.a.c

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} - q^{5} + 2q^{6} - 4q^{7} + q^{8} + q^{9} - q^{10} - 2q^{11} + 2q^{12} - q^{13} - 4q^{14} - 2q^{15} + q^{16} + 2q^{17} + q^{18} + 6q^{19} + O(q^{20})$$ ## 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. 