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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 348726.by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
348726.by1 | 348726by1 | \([1, 1, 1, -1518, 20523]\) | \(56402207875/4451328\) | \(30531658752\) | \([2]\) | \(307200\) | \(0.75560\) | \(\Gamma_0(N)\)-optimal |
348726.by2 | 348726by2 | \([1, 1, 1, 1522, 95915]\) | \(56844576125/604685088\) | \(-4147535018592\) | \([2]\) | \(614400\) | \(1.1022\) |
Rank
sage: E.rank()
The elliptic curves in class 348726.by have rank \(1\).
Complex multiplication
The elliptic curves in class 348726.by do not have complex multiplication.Modular form 348726.2.a.by
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.