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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 26928.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26928.c1 | 26928c2 | \([0, 0, 0, -179547, -19435910]\) | \(23152316479601292/7495915709689\) | \(207247077541481472\) | \([2]\) | \(471040\) | \(2.0261\) | |
26928.c2 | 26928c1 | \([0, 0, 0, -162207, -25140770]\) | \(68285541719739888/13451140571\) | \(92974283626752\) | \([2]\) | \(235520\) | \(1.6795\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26928.c have rank \(0\).
Complex multiplication
The elliptic curves in class 26928.c do not have complex multiplication.Modular form 26928.2.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.