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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 162240.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.h1 | 162240dj4 | \([0, -1, 0, -849281, -300921375]\) | \(428320044872/73125\) | \(11565806653440000\) | \([2]\) | \(2064384\) | \(2.0888\) | |
| 162240.h2 | 162240dj3 | \([0, -1, 0, -362561, 81299841]\) | \(33324076232/1285245\) | \(203280617740861440\) | \([2]\) | \(2064384\) | \(2.0888\) | |
| 162240.h3 | 162240dj2 | \([0, -1, 0, -58361, -3693639]\) | \(1111934656/342225\) | \(6765996892262400\) | \([2, 2]\) | \(1032192\) | \(1.7422\) | |
| 162240.h4 | 162240dj1 | \([0, -1, 0, 10084, -394590]\) | \(367061696/426465\) | \(-131741766411840\) | \([2]\) | \(516096\) | \(1.3956\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162240.h have rank \(0\).
Complex multiplication
The elliptic curves in class 162240.h do not have complex multiplication.Modular form 162240.2.a.h
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.
