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SageMath
E = EllipticCurve("hv1")
E.isogeny_class()
Elliptic curves in class 379050.hv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
379050.hv1 | 379050hv2 | \([1, 1, 1, -126538, 18278231]\) | \(-7620530425/526848\) | \(-15491267695680000\) | \([]\) | \(4478976\) | \(1.8575\) | |
379050.hv2 | 379050hv1 | \([1, 1, 1, 8837, 29681]\) | \(2595575/1512\) | \(-44458357545000\) | \([]\) | \(1492992\) | \(1.3082\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 379050.hv have rank \(1\).
Complex multiplication
The elliptic curves in class 379050.hv do not have complex multiplication.Modular form 379050.2.a.hv
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.