# Properties

 Label 1950.c Number of curves $2$ Conductor $1950$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1950.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.c1 1950e2 $$[1, 1, 0, -160, -200]$$ $$3659383421/2056392$$ $$257049000$$ $$$$ $$768$$ $$0.30386$$
1950.c2 1950e1 $$[1, 1, 0, 40, 0]$$ $$54439939/32448$$ $$-4056000$$ $$$$ $$384$$ $$-0.042709$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1950.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1950.c do not have complex multiplication.

## Modular form1950.2.a.c

sage: E.q_eigenform(10)

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