Properties

 Label 435.c Number of curves $2$ Conductor $435$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
E = EllipticCurve("c1")

E.isogeny_class()

Elliptic curves in class 435.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435.c1 435a1 $$[0, 1, 1, -11, 11]$$ $$-160989184/3915$$ $$-3915$$ $$[3]$$ $$20$$ $$-0.52517$$ $$\Gamma_0(N)$$-optimal
435.c2 435a2 $$[0, 1, 1, 49, 80]$$ $$12747309056/9145875$$ $$-9145875$$ $$[]$$ $$60$$ $$0.024133$$

Rank

sage: E.rank()

The elliptic curves in class 435.c have rank $$0$$.

Complex multiplication

The elliptic curves in class 435.c do not have complex multiplication.

Modular form435.2.a.c

sage: E.q_eigenform(10)

$$q + q^{3} - 2 q^{4} - q^{5} + 2 q^{7} + q^{9} + 3 q^{11} - 2 q^{12} + 2 q^{13} - q^{15} + 4 q^{16} + 2 q^{19} + O(q^{20})$$

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.