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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 46800.ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.ce1 | 46800cy2 | \([0, 0, 0, -49800, -4884500]\) | \(-4684079104/823875\) | \(-2402419500000000\) | \([]\) | \(165888\) | \(1.6770\) | |
46800.ce2 | 46800cy1 | \([0, 0, 0, 4200, 29500]\) | \(2809856/1755\) | \(-5117580000000\) | \([]\) | \(55296\) | \(1.1277\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.ce have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.ce do not have complex multiplication.Modular form 46800.2.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.