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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 188760.cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 188760.cg1 | 188760bq2 | \([0, 1, 0, -99829880, -271404080400]\) | \(22784591413352662/6597644551875\) | \(31860532709647126467840000\) | \([2]\) | \(72382464\) | \(3.5998\) | |
| 188760.cg2 | 188760bq1 | \([0, 1, 0, 16606000, -28099665552]\) | \(209741642018356/262704572325\) | \(-634310287082369281612800\) | \([2]\) | \(36191232\) | \(3.2533\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 188760.cg have rank \(0\).
Complex multiplication
The elliptic curves in class 188760.cg do not have complex multiplication.Modular form 188760.2.a.cg
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.
