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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 90506.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
90506.a1 | 90506b2 | \([1, -1, 0, -740365, 269212327]\) | \(-1064019559329/125497034\) | \(-5293531864482720794\) | \([]\) | \(2842000\) | \(2.3286\) | |
90506.a2 | 90506b1 | \([1, -1, 0, -9355, -530363]\) | \(-2146689/1664\) | \(-70188407978624\) | \([]\) | \(406000\) | \(1.3556\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 90506.a have rank \(1\).
Complex multiplication
The elliptic curves in class 90506.a do not have complex multiplication.Modular form 90506.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.