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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 26026.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26026.l1 | 26026i4 | \([1, -1, 1, -278206, -56409895]\) | \(493357359497913/8796788\) | \(42460415489492\) | \([2]\) | \(129024\) | \(1.7421\) | |
| 26026.l2 | 26026i2 | \([1, -1, 1, -17946, -818359]\) | \(132417047673/16032016\) | \(77383479116944\) | \([2, 2]\) | \(64512\) | \(1.3955\) | |
| 26026.l3 | 26026i1 | \([1, -1, 1, -4426, 101001]\) | \(1986121593/256256\) | \(1236898767104\) | \([4]\) | \(32256\) | \(1.0490\) | \(\Gamma_0(N)\)-optimal |
| 26026.l4 | 26026i3 | \([1, -1, 1, 25994, -4228103]\) | \(402437650887/1827958132\) | \(-8823204763160788\) | \([2]\) | \(129024\) | \(1.7421\) |
Rank
sage: E.rank()
The elliptic curves in class 26026.l have rank \(0\).
Complex multiplication
The elliptic curves in class 26026.l do not have complex multiplication.Modular form 26026.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
