Properties

 Label 7800.h Number of curves $2$ Conductor $7800$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

Elliptic curves in class 7800.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7800.h1 7800l2 $$[0, -1, 0, -5008, 136012]$$ $$434163602/7605$$ $$243360000000$$ $$$$ $$9216$$ $$0.98134$$
7800.h2 7800l1 $$[0, -1, 0, -8, 6012]$$ $$-4/975$$ $$-15600000000$$ $$$$ $$4608$$ $$0.63476$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 7800.h have rank $$0$$.

Complex multiplication

The elliptic curves in class 7800.h do not have complex multiplication.

Modular form7800.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} + 2 q^{7} + q^{9} - q^{13} + 4 q^{17} + 6 q^{19} + O(q^{20})$$ 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. 