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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 146523.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
146523.q1 | 146523q2 | \([0, -1, 1, -2897899, -1898853513]\) | \(-23100424192/14739\) | \(-1717203088699824219\) | \([]\) | \(4043520\) | \(2.4399\) | |
146523.q2 | 146523q1 | \([0, -1, 1, 32561, -10904658]\) | \(32768/459\) | \(-53476912796880339\) | \([]\) | \(1347840\) | \(1.8906\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 146523.q have rank \(1\).
Complex multiplication
The elliptic curves in class 146523.q do not have complex multiplication.Modular form 146523.2.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.