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SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 331056ew
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
331056.ew2 | 331056ew1 | \([0, 0, 0, 66429, -15176062]\) | \(165469149/603592\) | \(-118256030810210304\) | \([]\) | \(4147200\) | \(1.9589\) | \(\Gamma_0(N)\)-optimal |
331056.ew1 | 331056ew2 | \([0, 0, 0, -3244131, -2252746782]\) | \(-26436959739/50578\) | \(-7223854724195180544\) | \([]\) | \(12441600\) | \(2.5082\) |
Rank
sage: E.rank()
The elliptic curves in class 331056ew have rank \(0\).
Complex multiplication
The elliptic curves in class 331056ew do not have complex multiplication.Modular form 331056.2.a.ew
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.