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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 29601.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29601.h1 | 29601k2 | \([1, -1, 0, -74763, 7835854]\) | \(63395672188101553/475137974883\) | \(346375583689707\) | \([2]\) | \(113664\) | \(1.6201\) | |
29601.h2 | 29601k1 | \([1, -1, 0, -74628, 7865635]\) | \(63052870949070913/3581721\) | \(2611074609\) | \([2]\) | \(56832\) | \(1.2735\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29601.h have rank \(1\).
Complex multiplication
The elliptic curves in class 29601.h do not have complex multiplication.Modular form 29601.2.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.