# Properties

 Label 950.a Number of curves $2$ Conductor $950$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 950.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
950.a1 950b2 $$[1, 1, 0, -69500, -7081250]$$ $$-2376117230685121/342950$$ $$-5358593750$$ $$[]$$ $$1728$$ $$1.2759$$
950.a2 950b1 $$[1, 1, 0, -750, -12500]$$ $$-2992209121/2375000$$ $$-37109375000$$ $$[]$$ $$576$$ $$0.72655$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 950.a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 950.a do not have complex multiplication.

## Modular form950.2.a.a

sage: E.q_eigenform(10)

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