# Properties

 Label 1950.g Number of curves $2$ Conductor $1950$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1950.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.g1 1950l2 $$[1, 0, 1, -227451, -38491202]$$ $$666276475992821/58199166792$$ $$113670247640625000$$ $$[2]$$ $$30720$$ $$2.0132$$
1950.g2 1950l1 $$[1, 0, 1, -222451, -40401202]$$ $$623295446073461/5458752$$ $$10661625000000$$ $$[2]$$ $$15360$$ $$1.6667$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1950.2.a.g

sage: E.q_eigenform(10)

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

## 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.