# Properties

 Label 1950.f Number of curves $2$ Conductor $1950$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 1950.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.f1 1950m2 $$[1, 0, 1, -84076, -9391702]$$ $$-168256703745625/30371328$$ $$-11863800000000$$ $$[]$$ $$9720$$ $$1.5124$$
1950.f2 1950m1 $$[1, 0, 1, 299, -42952]$$ $$7604375/2047032$$ $$-799621875000$$ $$$$ $$3240$$ $$0.96312$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1950.f have rank $$0$$.

## Complex multiplication

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

## Modular form1950.2.a.f

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 