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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 384h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
384.e1 | 384h1 | \([0, 1, 0, -35, 69]\) | \(19056256/27\) | \(6912\) | \([2]\) | \(48\) | \(-0.36010\) | \(\Gamma_0(N)\)-optimal |
384.e2 | 384h2 | \([0, 1, 0, -25, 119]\) | \(-219488/729\) | \(-5971968\) | \([2]\) | \(96\) | \(-0.013528\) |
Rank
sage: E.rank()
The elliptic curves in class 384h have rank \(1\).
Complex multiplication
The elliptic curves in class 384h do not have complex multiplication.Modular form 384.2.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 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.