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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 90480.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90480.s1 | 90480bl4 | \([0, -1, 0, -150559240, -682367176400]\) | \(92148020139329101671876361/4210293743325439453125\) | \(17245363172661000000000000\) | \([4]\) | \(17694720\) | \(3.6043\) | |
| 90480.s2 | 90480bl2 | \([0, -1, 0, -148867960, -699066198608]\) | \(89077388930693421764046841/199454797863140625\) | \(816966852047424000000\) | \([2, 2]\) | \(8847360\) | \(3.2577\) | |
| 90480.s3 | 90480bl1 | \([0, -1, 0, -148867880, -699066987600]\) | \(89077245323151497432103721/446603625\) | \(1829288448000\) | \([2]\) | \(4423680\) | \(2.9111\) | \(\Gamma_0(N)\)-optimal |
| 90480.s4 | 90480bl3 | \([0, -1, 0, -147177960, -715714726608]\) | \(-86077987377718544995236841/4219867575452158651125\) | \(-17284577589052041835008000\) | \([2]\) | \(17694720\) | \(3.6043\) |
Rank
sage: E.rank()
The elliptic curves in class 90480.s have rank \(1\).
Complex multiplication
The elliptic curves in class 90480.s do not have complex multiplication.Modular form 90480.2.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.
