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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 17850.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17850.bd1 | 17850be2 | \([1, 1, 1, -1148, -89059]\) | \(-6693187811305/131714173248\) | \(-3292854331200\) | \([]\) | \(38880\) | \(1.0829\) | |
17850.bd2 | 17850be1 | \([1, 1, 1, 127, 3251]\) | \(9056932295/181997172\) | \(-4549929300\) | \([]\) | \(12960\) | \(0.53356\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17850.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 17850.bd do not have complex multiplication.Modular form 17850.2.a.bd
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.