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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 24336.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24336.f1 | 24336ch2 | \([0, 0, 0, -7836699, 8585036746]\) | \(-1680914269/32768\) | \(-1037594311255262232576\) | \([]\) | \(1123200\) | \(2.8261\) | |
24336.f2 | 24336ch1 | \([0, 0, 0, 72501, -23020166]\) | \(1331/8\) | \(-253318923646304256\) | \([]\) | \(224640\) | \(2.0214\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24336.f have rank \(0\).
Complex multiplication
The elliptic curves in class 24336.f do not have complex multiplication.Modular form 24336.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.