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SageMath
E = EllipticCurve("oy1")
E.isogeny_class()
Elliptic curves in class 158400.oy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
158400.oy1 | 158400fw1 | \([0, 0, 0, -1274700, 559226000]\) | \(-76711450249/851840\) | \(-2543580610560000000\) | \([]\) | \(3870720\) | \(2.3466\) | \(\Gamma_0(N)\)-optimal |
158400.oy2 | 158400fw2 | \([0, 0, 0, 4269300, 2898794000]\) | \(2882081488391/2883584000\) | \(-8610335686656000000000\) | \([]\) | \(11612160\) | \(2.8959\) |
Rank
sage: E.rank()
The elliptic curves in class 158400.oy have rank \(1\).
Complex multiplication
The elliptic curves in class 158400.oy do not have complex multiplication.Modular form 158400.2.a.oy
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.