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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 266616.cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
266616.cb1 | 266616cb2 | \([0, 0, 0, -58719, -5475150]\) | \(21882096/7\) | \(7162568453376\) | \([2]\) | \(760320\) | \(1.4414\) | |
266616.cb2 | 266616cb1 | \([0, 0, 0, -3174, -109503]\) | \(-55296/49\) | \(-3133623698352\) | \([2]\) | \(380160\) | \(1.0949\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 266616.cb have rank \(1\).
Complex multiplication
The elliptic curves in class 266616.cb do not have complex multiplication.Modular form 266616.2.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.