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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 29624.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29624.p1 | 29624d2 | \([0, -1, 0, -21336, 1192268]\) | \(3543122/49\) | \(14855697532928\) | \([2]\) | \(90112\) | \(1.3331\) | |
29624.p2 | 29624d1 | \([0, -1, 0, -176, 49628]\) | \(-4/7\) | \(-1061121252352\) | \([2]\) | \(45056\) | \(0.98650\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29624.p have rank \(0\).
Complex multiplication
The elliptic curves in class 29624.p do not have complex multiplication.Modular form 29624.2.a.p
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.