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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 14490.cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.cb1 | 14490cb1 | \([1, -1, 1, -212, -601]\) | \(1439069689/579600\) | \(422528400\) | \([2]\) | \(6144\) | \(0.35311\) | \(\Gamma_0(N)\)-optimal |
14490.cb2 | 14490cb2 | \([1, -1, 1, 688, -4921]\) | \(49471280711/41992020\) | \(-30612182580\) | \([2]\) | \(12288\) | \(0.69968\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.cb have rank \(0\).
Complex multiplication
The elliptic curves in class 14490.cb do not have complex multiplication.Modular form 14490.2.a.cb
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.