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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 255024.ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
255024.ci1 | 255024ci2 | \([0, 0, 0, -4389944672595, -3540272435937958894]\) | \(-3133382230165522315000208250857964625/153574604080128\) | \(-458571310589596925952\) | \([]\) | \(1724405760\) | \(5.3569\) | |
255024.ci2 | 255024ci1 | \([0, 0, 0, -54196371795, -4856430362500078]\) | \(-5895856113332931416918127084625/215771481613620039647232\) | \(-644290191754563620466000396288\) | \([]\) | \(574801920\) | \(4.8076\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 255024.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 255024.ci do not have complex multiplication.Modular form 255024.2.a.ci
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.