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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 3234.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3234.h1 | 3234i1 | \([1, 0, 1, -565, 7592]\) | \(-3451273/2376\) | \(-13697167176\) | \([3]\) | \(3024\) | \(0.64536\) | \(\Gamma_0(N)\)-optimal |
3234.h2 | 3234i2 | \([1, 0, 1, 4580, -113830]\) | \(1843623047/2044416\) | \(-11785651401216\) | \([]\) | \(9072\) | \(1.1947\) |
Rank
sage: E.rank()
The elliptic curves in class 3234.h have rank \(0\).
Complex multiplication
The elliptic curves in class 3234.h do not have complex multiplication.Modular form 3234.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.