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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 211600.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
211600.q1 | 211600q2 | \([0, 1, 0, -14657708, -21361913912]\) | \(941054800/12167\) | \(4502881653657500000000\) | \([]\) | \(15966720\) | \(2.9632\) | |
211600.q2 | 211600q1 | \([0, 1, 0, -1432708, 644486088]\) | \(878800/23\) | \(8512063617500000000\) | \([]\) | \(5322240\) | \(2.4139\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 211600.q have rank \(1\).
Complex multiplication
The elliptic curves in class 211600.q do not have complex multiplication.Modular form 211600.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.