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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 96330.cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96330.cm1 | 96330ct2 | \([1, 1, 1, -273530, 54947927]\) | \(468898230633769/5540400\) | \(26742452583600\) | \([2]\) | \(903168\) | \(1.7265\) | |
96330.cm2 | 96330ct1 | \([1, 1, 1, -16650, 900375]\) | \(-105756712489/12476160\) | \(-60220041373440\) | \([2]\) | \(451584\) | \(1.3799\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 96330.cm have rank \(0\).
Complex multiplication
The elliptic curves in class 96330.cm do not have complex multiplication.Modular form 96330.2.a.cm
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.