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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 111090.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111090.be1 | 111090be1 | \([1, 0, 1, -12443, -295594]\) | \(1439069689/579600\) | \(85801601264400\) | \([2]\) | \(405504\) | \(1.3715\) | \(\Gamma_0(N)\)-optimal |
111090.be2 | 111090be2 | \([1, 0, 1, 40457, -2136514]\) | \(49471280711/41992020\) | \(-6216326011605780\) | \([2]\) | \(811008\) | \(1.7181\) |
Rank
sage: E.rank()
The elliptic curves in class 111090.be have rank \(0\).
Complex multiplication
The elliptic curves in class 111090.be do not have complex multiplication.Modular form 111090.2.a.be
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.