Properties

 Label 62400.i Number of curves $2$ Conductor $62400$ CM no Rank $2$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

Elliptic curves in class 62400.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.i1 62400fy2 $$[0, -1, 0, -993, 4257]$$ $$26463592/13689$$ $$56070144000$$ $$[2]$$ $$57344$$ $$0.75452$$
62400.i2 62400fy1 $$[0, -1, 0, -793, 8857]$$ $$107850176/117$$ $$59904000$$ $$[2]$$ $$28672$$ $$0.40795$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 62400.i have rank $$2$$.

Complex multiplication

The elliptic curves in class 62400.i do not have complex multiplication.

Modular form 62400.2.a.i

sage: E.q_eigenform(10)

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

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.