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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 155526.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155526.i1 | 155526cz2 | \([1, 1, 0, -9345060, 10822819176]\) | \(5182207647625/91449288\) | \(1592705884801378317768\) | \([2]\) | \(9732096\) | \(2.8645\) | |
155526.i2 | 155526cz1 | \([1, 1, 0, -13500, 485317008]\) | \(-15625/5842368\) | \(-101752283678526387648\) | \([2]\) | \(4866048\) | \(2.5180\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 155526.i have rank \(1\).
Complex multiplication
The elliptic curves in class 155526.i do not have complex multiplication.Modular form 155526.2.a.i
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.