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SageMath
E = EllipticCurve("oa1")
E.isogeny_class()
Elliptic curves in class 176400.oa
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.oa1 | 176400mn1 | \([0, 0, 0, -6803895, 6830999350]\) | \(12692020761488/9261\) | \(25416961490592000\) | \([2]\) | \(3538944\) | \(2.4589\) | \(\Gamma_0(N)\)-optimal |
176400.oa2 | 176400mn2 | \([0, 0, 0, -6759795, 6923918050]\) | \(-3111705953492/85766121\) | \(-941545921457490048000\) | \([2]\) | \(7077888\) | \(2.8055\) |
Rank
sage: E.rank()
The elliptic curves in class 176400.oa have rank \(0\).
Complex multiplication
The elliptic curves in class 176400.oa do not have complex multiplication.Modular form 176400.2.a.oa
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.