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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 92400w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.dj3 | 92400w1 | \([0, -1, 0, -98473908, -376083914688]\) | \(26401417552259125806544/507547744790625\) | \(2030190979162500000000\) | \([2]\) | \(11796480\) | \(3.2115\) | \(\Gamma_0(N)\)-optimal |
| 92400.dj2 | 92400w2 | \([0, -1, 0, -101754408, -349682450688]\) | \(7282213870869695463556/912102595400390625\) | \(14593641526406250000000000\) | \([2, 2]\) | \(23592960\) | \(3.5581\) | |
| 92400.dj4 | 92400w3 | \([0, -1, 0, 151370592, -1812744950688]\) | \(11986661998777424518222/51295853620928503125\) | \(-1641467315869712100000000000\) | \([4]\) | \(47185920\) | \(3.9047\) | |
| 92400.dj1 | 92400w4 | \([0, -1, 0, -407367408, 2803021257312]\) | \(233632133015204766393938/29145526885986328125\) | \(932656860351562500000000000\) | \([2]\) | \(47185920\) | \(3.9047\) |
Rank
sage: E.rank()
The elliptic curves in class 92400w have rank \(1\).
Complex multiplication
The elliptic curves in class 92400w do not have complex multiplication.Modular form 92400.2.a.w
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.
