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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 39600.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.bc1 | 39600j1 | \([0, 0, 0, -8550, -293625]\) | \(379275264/15125\) | \(2756531250000\) | \([2]\) | \(73728\) | \(1.1536\) | \(\Gamma_0(N)\)-optimal |
| 39600.bc2 | 39600j2 | \([0, 0, 0, 3825, -1073250]\) | \(2122416/171875\) | \(-501187500000000\) | \([2]\) | \(147456\) | \(1.5002\) |
Rank
sage: E.rank()
The elliptic curves in class 39600.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 39600.bc do not have complex multiplication.Modular form 39600.2.a.bc
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.
