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SageMath
E = EllipticCurve("caw1")
E.isogeny_class()
Elliptic curves in class 705600.caw
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.caw1 | \([0, 0, 0, -4050864300, 99236092686640]\) | \(266916252066900625/162\) | \(4461766039948492800\) | \([]\) | \(278691840\) | \(3.8012\) |
705600.caw2 | \([0, 0, 0, -50112300, 135545285680]\) | \(505318200625/4251528\) | \(117094587952408245043200\) | \([]\) | \(92897280\) | \(3.2519\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.caw have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.caw do not have complex multiplication.Modular form 705600.2.a.caw
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.