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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 297024o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 297024.o4 | 297024o1 | \([0, -1, 0, -7287649, 7015713793]\) | \(163284962754131070553/13437317849509008\) | \(3522512250341689393152\) | \([2]\) | \(17694720\) | \(2.8769\) | \(\Gamma_0(N)\)-optimal |
| 297024.o2 | 297024o2 | \([0, -1, 0, -114194529, 469730071809]\) | \(628231468580531210149273/4842372001819716\) | \(1269398766045027631104\) | \([2, 2]\) | \(35389440\) | \(3.2235\) | |
| 297024.o1 | 297024o3 | \([0, -1, 0, -1827109089, 30061014261633]\) | \(2573221814539797208162915513/152882977338\) | \(40077355211292672\) | \([4]\) | \(70778880\) | \(3.5700\) | |
| 297024.o3 | 297024o4 | \([0, -1, 0, -111790049, 490454284929]\) | \(-589377067550053459948153/55271687920559220474\) | \(-14489141358247076291936256\) | \([2]\) | \(70778880\) | \(3.5700\) |
Rank
sage: E.rank()
The elliptic curves in class 297024o have rank \(0\).
Complex multiplication
The elliptic curves in class 297024o do not have complex multiplication.Modular form 297024.2.a.o
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.
