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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 39600.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39600.i1 | 39600bu2 | \([0, 0, 0, -795, -6950]\) | \(595508/121\) | \(11290752000\) | \([2]\) | \(30720\) | \(0.64462\) | |
39600.i2 | 39600bu1 | \([0, 0, 0, 105, -650]\) | \(5488/11\) | \(-256608000\) | \([2]\) | \(15360\) | \(0.29804\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39600.i have rank \(2\).
Complex multiplication
The elliptic curves in class 39600.i do not have complex multiplication.Modular form 39600.2.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.