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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 29744.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29744.y1 | 29744z3 | \([0, 1, 0, -21146181, 37420901363]\) | \(-52893159101157376/11\) | \(-217476706304\) | \([]\) | \(432000\) | \(2.4723\) | |
29744.y2 | 29744z2 | \([0, 1, 0, -27941, 3246803]\) | \(-122023936/161051\) | \(-3184076456996864\) | \([]\) | \(86400\) | \(1.6676\) | |
29744.y3 | 29744z1 | \([0, 1, 0, -901, -25037]\) | \(-4096/11\) | \(-217476706304\) | \([]\) | \(17280\) | \(0.86289\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29744.y have rank \(1\).
Complex multiplication
The elliptic curves in class 29744.y do not have complex multiplication.Modular form 29744.2.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 LMFDB numbering.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.