Properties

 Label 1850.a Number of curves $2$ Conductor $1850$ CM no Rank $1$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 1850.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1850.a1 1850g1 $$[1, 0, 1, -476, 9498]$$ $$-19026212425/51868672$$ $$-32417920000$$ $$$$ $$1800$$ $$0.70419$$ $$\Gamma_0(N)$$-optimal
1850.a2 1850g2 $$[1, 0, 1, 4149, -216202]$$ $$12642252501575/39728447488$$ $$-24830279680000$$ $$[]$$ $$5400$$ $$1.2535$$

Rank

sage: E.rank()

The elliptic curves in class 1850.a have rank $$1$$.

Complex multiplication

The elliptic curves in class 1850.a do not have complex multiplication.

Modular form1850.2.a.a

sage: E.q_eigenform(10)

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