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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 323400.ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
323400.ct1 | 323400ct2 | \([0, -1, 0, -21968, 982332]\) | \(77860436/17787\) | \(267855713664000\) | \([2]\) | \(884736\) | \(1.4809\) | |
323400.ct2 | 323400ct1 | \([0, -1, 0, -7268, -223068]\) | \(11279504/693\) | \(2608984224000\) | \([2]\) | \(442368\) | \(1.1344\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 323400.ct have rank \(1\).
Complex multiplication
The elliptic curves in class 323400.ct do not have complex multiplication.Modular form 323400.2.a.ct
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.