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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 50400.cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50400.cp1 | 50400bs4 | \([0, 0, 0, -71442300, 232424152000]\) | \(864335783029582144/59535\) | \(2777664960000000\) | \([2]\) | \(2949120\) | \(2.8643\) | |
| 50400.cp2 | 50400bs3 | \([0, 0, 0, -5016675, 2678035750]\) | \(2394165105226952/854262178245\) | \(4982057023524840000000\) | \([2]\) | \(2949120\) | \(2.8643\) | |
| 50400.cp3 | 50400bs1 | \([0, 0, 0, -4465425, 3631147000]\) | \(13507798771700416/3544416225\) | \(2583879428025000000\) | \([2, 2]\) | \(1474560\) | \(2.5177\) | \(\Gamma_0(N)\)-optimal |
| 50400.cp4 | 50400bs2 | \([0, 0, 0, -3918675, 4553514250]\) | \(-1141100604753992/875529151875\) | \(-5106086013735000000000\) | \([2]\) | \(2949120\) | \(2.8643\) |
Rank
sage: E.rank()
The elliptic curves in class 50400.cp have rank \(1\).
Complex multiplication
The elliptic curves in class 50400.cp do not have complex multiplication.Modular form 50400.2.a.cp
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.
