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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 26520.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26520.q1 | 26520b4 | \([0, -1, 0, -254600, -49361748]\) | \(891190736491222802/3729375\) | \(7637760000\) | \([2]\) | \(122880\) | \(1.5279\) | |
26520.q2 | 26520b2 | \([0, -1, 0, -15920, -766500]\) | \(435792975088324/890127225\) | \(911490278400\) | \([2, 2]\) | \(61440\) | \(1.1813\) | |
26520.q3 | 26520b3 | \([0, -1, 0, -10520, -1300020]\) | \(-62875617222962/322034842935\) | \(-659527358330880\) | \([2]\) | \(122880\) | \(1.5279\) | |
26520.q4 | 26520b1 | \([0, -1, 0, -1340, -2508]\) | \(1040212820176/587242305\) | \(150334030080\) | \([2]\) | \(30720\) | \(0.83471\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26520.q have rank \(0\).
Complex multiplication
The elliptic curves in class 26520.q do not have complex multiplication.Modular form 26520.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.