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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 284592.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
284592.bl1 | 284592bl2 | \([0, -1, 0, -86547589, -310126549907]\) | \(-1713910976512/1594323\) | \(-66692452844507556261888\) | \([]\) | \(30576000\) | \(3.3024\) | |
284592.bl2 | 284592bl1 | \([0, -1, 0, -221349, 43630413]\) | \(-28672/3\) | \(-125493616120147968\) | \([]\) | \(2352000\) | \(2.0200\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 284592.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 284592.bl do not have complex multiplication.Modular form 284592.2.a.bl
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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.