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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 38829a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38829.a2 | 38829a1 | \([1, 1, 1, -6467, -202864]\) | \(376210684459/7203\) | \(572688921\) | \([2]\) | \(47872\) | \(0.80369\) | \(\Gamma_0(N)\)-optimal |
38829.a1 | 38829a2 | \([1, 1, 1, -6682, -188932]\) | \(414994003579/51883209\) | \(4125078297963\) | \([2]\) | \(95744\) | \(1.1503\) |
Rank
sage: E.rank()
The elliptic curves in class 38829a have rank \(1\).
Complex multiplication
The elliptic curves in class 38829a do not have complex multiplication.Modular form 38829.2.a.a
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 Cremona 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 Cremona labels.