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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 127296.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127296.c1 | 127296ck2 | \([0, 0, 0, -199092, 15636800]\) | \(292279034436544/133768319373\) | \(399430061354668032\) | \([2]\) | \(2064384\) | \(2.0723\) | |
127296.c2 | 127296ck1 | \([0, 0, 0, -100227, -12045400]\) | \(2386549263163456/37663590627\) | \(1757232484293312\) | \([2]\) | \(1032192\) | \(1.7257\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 127296.c have rank \(1\).
Complex multiplication
The elliptic curves in class 127296.c do not have complex multiplication.Modular form 127296.2.a.c
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.