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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 463680.ck
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
463680.ck1 | 463680ck1 | \([0, 0, 0, -13548, 334672]\) | \(1439069689/579600\) | \(110763284889600\) | \([2]\) | \(1179648\) | \(1.3928\) | \(\Gamma_0(N)\)-optimal |
463680.ck2 | 463680ck2 | \([0, 0, 0, 44052, 2431312]\) | \(49471280711/41992020\) | \(-8024799990251520\) | \([2]\) | \(2359296\) | \(1.7394\) |
Rank
sage: E.rank()
The elliptic curves in class 463680.ck have rank \(1\).
Complex multiplication
The elliptic curves in class 463680.ck do not have complex multiplication.Modular form 463680.2.a.ck
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.