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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 243360.cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
243360.cb1 | 243360cb2 | \([0, 0, 0, -529308, -134772768]\) | \(42144192/4225\) | \(1644137244819763200\) | \([2]\) | \(3096576\) | \(2.2316\) | |
243360.cb2 | 243360cb1 | \([0, 0, 0, 41067, -10202868]\) | \(1259712/8125\) | \(-49403162404440000\) | \([2]\) | \(1548288\) | \(1.8850\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 243360.cb have rank \(0\).
Complex multiplication
The elliptic curves in class 243360.cb do not have complex multiplication.Modular form 243360.2.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.