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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 94192o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
94192.s1 | 94192o1 | \([0, 1, 0, -195392, -330131404]\) | \(-338608873/19120976\) | \(-46586275615052988416\) | \([]\) | \(1935360\) | \(2.4539\) | \(\Gamma_0(N)\)-optimal |
94192.s2 | 94192o2 | \([0, 1, 0, 1755728, 8833108564]\) | \(245667233447/13974818816\) | \(-34048197175322246905856\) | \([]\) | \(5806080\) | \(3.0032\) |
Rank
sage: E.rank()
The elliptic curves in class 94192o have rank \(2\).
Complex multiplication
The elliptic curves in class 94192o do not have complex multiplication.Modular form 94192.2.a.o
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.