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SageMath
E = EllipticCurve("hu1")
E.isogeny_class()
Elliptic curves in class 127050.hu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127050.hu1 | 127050io2 | \([1, 0, 0, -42413, 3553617]\) | \(-7620530425/526848\) | \(-583339606080000\) | \([]\) | \(699840\) | \(1.5843\) | |
127050.hu2 | 127050io1 | \([1, 0, 0, 2962, 5292]\) | \(2595575/1512\) | \(-1674125145000\) | \([]\) | \(233280\) | \(1.0350\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 127050.hu have rank \(1\).
Complex multiplication
The elliptic curves in class 127050.hu do not have complex multiplication.Modular form 127050.2.a.hu
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.