Properties

 Label 1428.c Number of curves $2$ Conductor $1428$ CM no Rank $0$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 1428.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1428.c1 1428a1 $$[0, -1, 0, -337, -2270]$$ $$265327034368/297381$$ $$4758096$$ $$$$ $$360$$ $$0.19534$$ $$\Gamma_0(N)$$-optimal
1428.c2 1428a2 $$[0, -1, 0, -252, -3528]$$ $$-6940769488/18000297$$ $$-4608076032$$ $$$$ $$720$$ $$0.54191$$

Rank

sage: E.rank()

The elliptic curves in class 1428.c have rank $$0$$.

Complex multiplication

The elliptic curves in class 1428.c do not have complex multiplication.

Modular form1428.2.a.c

sage: E.q_eigenform(10)

$$q - q^{3} + 2 q^{5} - q^{7} + q^{9} + 6 q^{13} - 2 q^{15} - q^{17} - 2 q^{19} + O(q^{20})$$ 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 