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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 18032y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18032.p2 | 18032y1 | \([0, 1, 0, 82, 167]\) | \(32000/23\) | \(-43294832\) | \([]\) | \(2880\) | \(0.15369\) | \(\Gamma_0(N)\)-optimal |
18032.p1 | 18032y2 | \([0, 1, 0, -898, -12965]\) | \(-42592000/12167\) | \(-22902966128\) | \([]\) | \(8640\) | \(0.70299\) |
Rank
sage: E.rank()
The elliptic curves in class 18032y have rank \(0\).
Complex multiplication
The elliptic curves in class 18032y do not have complex multiplication.Modular form 18032.2.a.y
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.