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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 357390.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 357390.s1 | 357390s3 | \([1, -1, 0, -29639070, 62115026526]\) | \(83959202297868841/25036110\) | \(858649625935161390\) | \([2]\) | \(17694720\) | \(2.8060\) | |
| 357390.s2 | 357390s2 | \([1, -1, 0, -1860120, 962445996]\) | \(20753798525641/353816100\) | \(12134635209496908900\) | \([2, 2]\) | \(8847360\) | \(2.4594\) | |
| 357390.s3 | 357390s1 | \([1, -1, 0, -235620, -21026304]\) | \(42180533641/18810000\) | \(645116172753690000\) | \([2]\) | \(4423680\) | \(2.1129\) | \(\Gamma_0(N)\)-optimal |
| 357390.s4 | 357390s4 | \([1, -1, 0, -73170, 2732598666]\) | \(-1263214441/94053968910\) | \(-3225716983280901028590\) | \([2]\) | \(17694720\) | \(2.8060\) |
Rank
sage: E.rank()
The elliptic curves in class 357390.s have rank \(0\).
Complex multiplication
The elliptic curves in class 357390.s do not have complex multiplication.Modular form 357390.2.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 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.
