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SageMath
E = EllipticCurve("hv1")
E.isogeny_class()
Elliptic curves in class 179520hv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179520.t1 | 179520hv1 | \([0, -1, 0, -6561, 210465]\) | \(-119168121961/2524500\) | \(-661782528000\) | \([]\) | \(276480\) | \(1.0586\) | \(\Gamma_0(N)\)-optimal |
179520.t2 | 179520hv2 | \([0, -1, 0, 27039, 929505]\) | \(8339492177639/6277634880\) | \(-1645644317982720\) | \([]\) | \(829440\) | \(1.6079\) |
Rank
sage: E.rank()
The elliptic curves in class 179520hv have rank \(0\).
Complex multiplication
The elliptic curves in class 179520hv do not have complex multiplication.Modular form 179520.2.a.hv
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.