Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 219351.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 219351.h1 | 219351h1 | \([1, 1, 0, -12716150, 17448163383]\) | \(9421003472760015625/610453833\) | \(14734871515351977\) | \([2]\) | \(5971968\) | \(2.5608\) | \(\Gamma_0(N)\)-optimal |
| 219351.h2 | 219351h2 | \([1, 1, 0, -12691585, 17518964626]\) | \(-9366510526569933625/75850576475553\) | \(-1830848523368437350657\) | \([2]\) | \(11943936\) | \(2.9074\) |
Rank
sage: E.rank()
The elliptic curves in class 219351.h have rank \(2\).
Complex multiplication
The elliptic curves in class 219351.h do not have complex multiplication.Modular form 219351.2.a.h
sage: E.q_eigenform(10)
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.
