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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 212268h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
212268.bp2 | 212268h1 | \([0, 1, 0, -3369, 61116]\) | \(16384/3\) | \(774563384784\) | \([2]\) | \(290304\) | \(0.99987\) | \(\Gamma_0(N)\)-optimal |
212268.bp1 | 212268h2 | \([0, 1, 0, -16004, -727308]\) | \(109744/9\) | \(37179042469632\) | \([2]\) | \(580608\) | \(1.3464\) |
Rank
sage: E.rank()
The elliptic curves in class 212268h have rank \(1\).
Complex multiplication
The elliptic curves in class 212268h do not have complex multiplication.Modular form 212268.2.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.