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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 2070.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2070.q1 | 2070s2 | \([1, -1, 1, -15737, 669849]\) | \(591202341974089/79350000000\) | \(57846150000000\) | \([2]\) | \(7168\) | \(1.3682\) | |
2070.q2 | 2070s1 | \([1, -1, 1, 1543, 54681]\) | \(557644990391/2119680000\) | \(-1545246720000\) | \([2]\) | \(3584\) | \(1.0216\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2070.q have rank \(1\).
Complex multiplication
The elliptic curves in class 2070.q do not have complex multiplication.Modular form 2070.2.a.q
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.