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SageMath
E = EllipticCurve("gp1")
E.isogeny_class()
Elliptic curves in class 179520.gp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179520.gp1 | 179520ep2 | \([0, 1, 0, -9185, 213375]\) | \(326940373369/112003650\) | \(29361084825600\) | \([2]\) | \(393216\) | \(1.2862\) | |
179520.gp2 | 179520ep1 | \([0, 1, 0, 1695, 24063]\) | \(2053225511/2098140\) | \(-550014812160\) | \([2]\) | \(196608\) | \(0.93960\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 179520.gp have rank \(0\).
Complex multiplication
The elliptic curves in class 179520.gp do not have complex multiplication.Modular form 179520.2.a.gp
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.