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SageMath
E = EllipticCurve("ed1")
E.isogeny_class()
Elliptic curves in class 371280ed
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 371280.ed4 | 371280ed1 | \([0, 1, 0, -27769038456, 1021342524614100]\) | \(578157667940817624228325381788409/224561259415530338819315616000\) | \(919802918566012267803916763136000\) | \([2]\) | \(1521745920\) | \(5.0240\) | \(\Gamma_0(N)\)-optimal |
| 371280.ed2 | 371280ed2 | \([0, 1, 0, -389337357176, 93477688049850324]\) | \(1593463037319346477727119157097168889/546221162511858816329870250000\) | \(2237321881648573711687148544000000\) | \([2, 2]\) | \(3043491840\) | \(5.3706\) | |
| 371280.ed1 | 371280ed3 | \([0, 1, 0, -6228885136696, 5983612302074276180]\) | \(6525213578865970265696405437575208534969/767130688571676495117187500\) | \(3142167300389586924000000000000\) | \([2]\) | \(6086983680\) | \(5.7171\) | |
| 371280.ed3 | 371280ed4 | \([0, 1, 0, -334882677176, 120554972733642324]\) | \(-1014009007595272988562623757184248889/946022301497270062664245652323500\) | \(-3874907346932818176672750191917056000\) | \([2]\) | \(6086983680\) | \(5.7171\) |
Rank
sage: E.rank()
The elliptic curves in class 371280ed have rank \(0\).
Complex multiplication
The elliptic curves in class 371280ed do not have complex multiplication.Modular form 371280.2.a.ed
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
