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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 50430s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50430.t3 | 50430s1 | \([1, 1, 1, -867431, 250717853]\) | \(15195864748609/3060633600\) | \(14538328643507097600\) | \([2]\) | \(1935360\) | \(2.3929\) | \(\Gamma_0(N)\)-optimal |
| 50430.t4 | 50430s2 | \([1, 1, 1, 1822169, 1499768093]\) | \(140859621945791/285872742720\) | \(-1357925327580573875520\) | \([2]\) | \(3870720\) | \(2.7394\) | |
| 50430.t1 | 50430s3 | \([1, 1, 1, -21442871, -38205021571]\) | \(229545811016693569/155072250000\) | \(736609352386412250000\) | \([2]\) | \(5806080\) | \(2.9422\) | |
| 50430.t2 | 50430s4 | \([1, 1, 1, -17240371, -53621472571]\) | \(-119305480789133569/192379221760500\) | \(-913821357164830536280500\) | \([2]\) | \(11612160\) | \(3.2887\) |
Rank
sage: E.rank()
The elliptic curves in class 50430s have rank \(0\).
Complex multiplication
The elliptic curves in class 50430s do not have complex multiplication.Modular form 50430.2.a.s
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
