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SageMath
E = EllipticCurve("fb1")
E.isogeny_class()
Elliptic curves in class 46800.fb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.fb1 | 46800fp2 | \([0, 0, 0, -192000, -32290000]\) | \(671088640/2197\) | \(2562580800000000\) | \([]\) | \(388800\) | \(1.8221\) | |
46800.fb2 | 46800fp1 | \([0, 0, 0, -12000, 470000]\) | \(163840/13\) | \(15163200000000\) | \([]\) | \(129600\) | \(1.2727\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.fb have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.fb do not have complex multiplication.Modular form 46800.2.a.fb
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.