# Properties

 Label 350a Number of curves $4$ Conductor $350$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 350a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350.b4 350a1 $$[1, -1, 0, 58, -284]$$ $$1367631/2800$$ $$-43750000$$ $$$$ $$96$$ $$0.15056$$ $$\Gamma_0(N)$$-optimal
350.b3 350a2 $$[1, -1, 0, -442, -2784]$$ $$611960049/122500$$ $$1914062500$$ $$[2, 2]$$ $$192$$ $$0.49713$$
350.b1 350a3 $$[1, -1, 0, -6692, -209034]$$ $$2121328796049/120050$$ $$1875781250$$ $$$$ $$384$$ $$0.84371$$
350.b2 350a4 $$[1, -1, 0, -2192, 37466]$$ $$74565301329/5468750$$ $$85449218750$$ $$$$ $$384$$ $$0.84371$$

## Rank

sage: E.rank()

The elliptic curves in class 350a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 350a do not have complex multiplication.

## Modular form350.2.a.a

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 