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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 13552.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13552.w1 | 13552ba6 | \([0, -1, 0, -5286288, -4676390464]\) | \(2251439055699625/25088\) | \(182046402019328\) | \([2]\) | \(207360\) | \(2.3052\) | |
13552.w2 | 13552ba5 | \([0, -1, 0, -330128, -73109056]\) | \(-548347731625/1835008\) | \(-13315393976270848\) | \([2]\) | \(103680\) | \(1.9586\) | |
13552.w3 | 13552ba4 | \([0, -1, 0, -68768, -5666560]\) | \(4956477625/941192\) | \(6829584550756352\) | \([2]\) | \(69120\) | \(1.7559\) | |
13552.w4 | 13552ba2 | \([0, -1, 0, -20368, 1124928]\) | \(128787625/98\) | \(711118757888\) | \([2]\) | \(23040\) | \(1.2066\) | |
13552.w5 | 13552ba1 | \([0, -1, 0, -1008, 25280]\) | \(-15625/28\) | \(-203176787968\) | \([2]\) | \(11520\) | \(0.86001\) | \(\Gamma_0(N)\)-optimal |
13552.w6 | 13552ba3 | \([0, -1, 0, 8672, -524544]\) | \(9938375/21952\) | \(-159290601766912\) | \([2]\) | \(34560\) | \(1.4093\) |
Rank
sage: E.rank()
The elliptic curves in class 13552.w have rank \(0\).
Complex multiplication
The elliptic curves in class 13552.w do not have complex multiplication.Modular form 13552.2.a.w
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.