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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 91035.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91035.w1 | 91035bs2 | \([1, -1, 1, -201632, 34774724]\) | \(51520374361/212415\) | \(3737715473249415\) | \([2]\) | \(589824\) | \(1.8435\) | |
91035.w2 | 91035bs1 | \([1, -1, 1, -6557, 1065764]\) | \(-1771561/26775\) | \(-471140605871775\) | \([2]\) | \(294912\) | \(1.4969\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91035.w have rank \(0\).
Complex multiplication
The elliptic curves in class 91035.w do not have complex multiplication.Modular form 91035.2.a.w
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.