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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 50400.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50400.bc1 | 50400s4 | \([0, 0, 0, -3177075, -2179660250]\) | \(608119035935048/826875\) | \(4822335000000000\) | \([2]\) | \(589824\) | \(2.2836\) | |
| 50400.bc2 | 50400s3 | \([0, 0, 0, -504075, 92025250]\) | \(2428799546888/778248135\) | \(4538743123320000000\) | \([2]\) | \(589824\) | \(2.2836\) | |
| 50400.bc3 | 50400s1 | \([0, 0, 0, -200325, -33423500]\) | \(1219555693504/43758225\) | \(31899746025000000\) | \([2, 2]\) | \(294912\) | \(1.9370\) | \(\Gamma_0(N)\)-optimal |
| 50400.bc4 | 50400s2 | \([0, 0, 0, 75300, -118316000]\) | \(1012048064/130203045\) | \(-6074753267520000000\) | \([2]\) | \(589824\) | \(2.2836\) |
Rank
sage: E.rank()
The elliptic curves in class 50400.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 50400.bc do not have complex multiplication.Modular form 50400.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
