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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 195195.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
195195.h1 | 195195k2 | \([1, 0, 0, -66336, -4808259]\) | \(6688239997321/1806079275\) | \(8717599699283475\) | \([2]\) | \(1204224\) | \(1.7667\) | |
195195.h2 | 195195k1 | \([1, 0, 0, 10559, -486760]\) | \(26973008999/36891855\) | \(-178069937740695\) | \([2]\) | \(602112\) | \(1.4202\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 195195.h have rank \(2\).
Complex multiplication
The elliptic curves in class 195195.h do not have complex multiplication.Modular form 195195.2.a.h
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.