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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 5040.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5040.q1 | 5040b2 | \([0, 0, 0, -783, -4482]\) | \(10536048/4375\) | \(22044960000\) | \([2]\) | \(3072\) | \(0.68192\) | |
5040.q2 | 5040b1 | \([0, 0, 0, 162, -513]\) | \(1492992/1225\) | \(-385786800\) | \([2]\) | \(1536\) | \(0.33534\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5040.q have rank \(0\).
Complex multiplication
The elliptic curves in class 5040.q do not have complex multiplication.Modular form 5040.2.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.