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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 2790.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2790.i1 | 2790c1 | \([1, -1, 0, -118599, -9168707]\) | \(6832900384593441003/2600468480000000\) | \(70212648960000000\) | \([2]\) | \(33600\) | \(1.9319\) | \(\Gamma_0(N)\)-optimal |
2790.i2 | 2790c2 | \([1, -1, 0, 372921, -65890115]\) | \(212427047662836354837/192200000000000000\) | \(-5189400000000000000\) | \([2]\) | \(67200\) | \(2.2784\) |
Rank
sage: E.rank()
The elliptic curves in class 2790.i have rank \(0\).
Complex multiplication
The elliptic curves in class 2790.i do not have complex multiplication.Modular form 2790.2.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.