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SageMath
E = EllipticCurve("qc1")
E.isogeny_class()
Elliptic curves in class 176400.qc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.qc1 | 176400hz2 | \([0, 0, 0, -1767675, -904625750]\) | \(-5452947409/250\) | \(-28005264000000000\) | \([]\) | \(2488320\) | \(2.2316\) | |
176400.qc2 | 176400hz1 | \([0, 0, 0, -3675, -3221750]\) | \(-49/40\) | \(-4480842240000000\) | \([]\) | \(829440\) | \(1.6823\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.qc have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.qc do not have complex multiplication.Modular form 176400.2.a.qc
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.