Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 47610l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47610.h4 | 47610l1 | \([1, -1, 0, -21381750, -67606919564]\) | \(-10017490085065009/12502381363200\) | \(-1349234030854672692019200\) | \([2]\) | \(7569408\) | \(3.3235\) | \(\Gamma_0(N)\)-optimal |
| 47610.h3 | 47610l2 | \([1, -1, 0, -411402870, -3210319100300]\) | \(71356102305927901489/35540674560000\) | \(3835484313174827919360000\) | \([2, 2]\) | \(15138816\) | \(3.6701\) | |
| 47610.h2 | 47610l3 | \([1, -1, 0, -481484790, -2041927346444]\) | \(114387056741228939569/49503729150000000\) | \(5342351515527353511150000000\) | \([2]\) | \(30277632\) | \(4.0167\) | |
| 47610.h1 | 47610l4 | \([1, -1, 0, -6581658870, -205516970674700]\) | \(292169767125103365085489/72534787200\) | \(7827820994095231363200\) | \([2]\) | \(30277632\) | \(4.0167\) |
Rank
sage: E.rank()
The elliptic curves in class 47610l have rank \(1\).
Complex multiplication
The elliptic curves in class 47610l do not have complex multiplication.Modular form 47610.2.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 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.
