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SageMath
E = EllipticCurve("jq1")
E.isogeny_class()
Elliptic curves in class 277200.jq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.jq1 | 277200jq6 | \([0, 0, 0, -10977120075, -442670657687750]\) | \(3135316978843283198764801/571725\) | \(26674401600000000\) | \([2]\) | \(94371840\) | \(3.9463\) | |
| 277200.jq2 | 277200jq4 | \([0, 0, 0, -686070075, -6916727537750]\) | \(765458482133960722801/326869475625\) | \(15250422254760000000000\) | \([2, 2]\) | \(47185920\) | \(3.5997\) | |
| 277200.jq3 | 277200jq5 | \([0, 0, 0, -682668075, -6988717259750]\) | \(-754127868744065783521/15825714261328125\) | \(-738364524576525000000000000\) | \([2]\) | \(94371840\) | \(3.9463\) | |
| 277200.jq4 | 277200jq3 | \([0, 0, 0, -91602075, 177951690250]\) | \(1821931919215868881/761147600816295\) | \(35512102463685059520000000\) | \([2]\) | \(47185920\) | \(3.5997\) | |
| 277200.jq5 | 277200jq2 | \([0, 0, 0, -43092075, -106947539750]\) | \(189674274234120481/3859869269025\) | \(180086060615630400000000\) | \([2, 2]\) | \(23592960\) | \(3.2532\) | |
| 277200.jq6 | 277200jq1 | \([0, 0, 0, 125925, -4996277750]\) | \(4733169839/231139696095\) | \(-10784053661008320000000\) | \([2]\) | \(11796480\) | \(2.9066\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277200.jq have rank \(0\).
Complex multiplication
The elliptic curves in class 277200.jq do not have complex multiplication.Modular form 277200.2.a.jq
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
