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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 20400.ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20400.ce1 | 20400dm2 | \([0, 1, 0, -23733, 1400163]\) | \(-23100424192/14739\) | \(-943296000000\) | \([]\) | \(46656\) | \(1.2386\) | |
20400.ce2 | 20400dm1 | \([0, 1, 0, 267, 8163]\) | \(32768/459\) | \(-29376000000\) | \([]\) | \(15552\) | \(0.68934\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20400.ce have rank \(0\).
Complex multiplication
The elliptic curves in class 20400.ce do not have complex multiplication.Modular form 20400.2.a.ce
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.