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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 152592.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152592.bp1 | 152592a1 | \([0, 1, 0, -906400, 331632884]\) | \(832972004929/610368\) | \(60345547634245632\) | \([2]\) | \(2654208\) | \(2.1541\) | \(\Gamma_0(N)\)-optimal |
152592.bp2 | 152592a2 | \([0, 1, 0, -721440, 471092724]\) | \(-420021471169/727634952\) | \(-71939435973475074048\) | \([2]\) | \(5308416\) | \(2.5007\) |
Rank
sage: E.rank()
The elliptic curves in class 152592.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 152592.bp do not have complex multiplication.Modular form 152592.2.a.bp
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.