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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 56550.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56550.i1 | 56550l2 | \([1, 1, 0, -2412950, 942556500]\) | \(795497689530094517/263435341962624\) | \(514522152270750000000\) | \([2]\) | \(3655680\) | \(2.6770\) | |
56550.i2 | 56550l1 | \([1, 1, 0, -2172950, 1231756500]\) | \(580955924718082997/122133233664\) | \(238541472000000000\) | \([2]\) | \(1827840\) | \(2.3304\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 56550.i have rank \(0\).
Complex multiplication
The elliptic curves in class 56550.i do not have complex multiplication.Modular form 56550.2.a.i
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.