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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 4650.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4650.q1 | 4650v1 | \([1, 0, 1, -576, 13798]\) | \(-53969305/180792\) | \(-70621875000\) | \([3]\) | \(4320\) | \(0.76793\) | \(\Gamma_0(N)\)-optimal |
4650.q2 | 4650v2 | \([1, 0, 1, 5049, -323702]\) | \(36450495095/137276928\) | \(-53623800000000\) | \([]\) | \(12960\) | \(1.3172\) |
Rank
sage: E.rank()
The elliptic curves in class 4650.q have rank \(0\).
Complex multiplication
The elliptic curves in class 4650.q do not have complex multiplication.Modular form 4650.2.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.