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SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 262080ew
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
262080.ew1 | 262080ew1 | \([0, 0, 0, -486828, 130740048]\) | \(267080942160036/1990625\) | \(95103590400000\) | \([2]\) | \(2293760\) | \(1.8581\) | \(\Gamma_0(N)\)-optimal |
262080.ew2 | 262080ew2 | \([0, 0, 0, -476748, 136413072]\) | \(-125415986034978/11552734375\) | \(-1103880960000000000\) | \([2]\) | \(4587520\) | \(2.2047\) |
Rank
sage: E.rank()
The elliptic curves in class 262080ew have rank \(0\).
Complex multiplication
The elliptic curves in class 262080ew do not have complex multiplication.Modular form 262080.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.