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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 405600eh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405600.eh1 | 405600eh1 | \([0, 1, 0, -12262358, 16518613788]\) | \(42246001231552/14414517\) | \(69576120386253000000\) | \([2]\) | \(16515072\) | \(2.7790\) | \(\Gamma_0(N)\)-optimal |
405600.eh2 | 405600eh2 | \([0, 1, 0, -10551233, 21294363663]\) | \(-420526439488/390971529\) | \(-120777273274941504000000\) | \([2]\) | \(33030144\) | \(3.1256\) |
Rank
sage: E.rank()
The elliptic curves in class 405600eh have rank \(1\).
Complex multiplication
The elliptic curves in class 405600eh do not have complex multiplication.Modular form 405600.2.a.eh
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 Cremona 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 Cremona labels.