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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 234432.cl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
234432.cl1 | 234432cl2 | \([0, 0, 0, -5645820, -5163434192]\) | \(1666315860501346000/40252707\) | \(480775756234752\) | \([2]\) | \(2949120\) | \(2.3372\) | |
234432.cl2 | 234432cl1 | \([0, 0, 0, -353280, -80478776]\) | \(6532108386304000/31987847133\) | \(23878799933395968\) | \([2]\) | \(1474560\) | \(1.9907\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 234432.cl have rank \(0\).
Complex multiplication
The elliptic curves in class 234432.cl do not have complex multiplication.Modular form 234432.2.a.cl
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.