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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 35574.cn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35574.cn1 | 35574de4 | \([1, 0, 0, -545494804, 4903768674608]\) | \(86129359107301290313/9166294368\) | \(1910460888774956038752\) | \([2]\) | \(11059200\) | \(3.5112\) | |
| 35574.cn2 | 35574de2 | \([1, 0, 0, -34177844, 76220728464]\) | \(21184262604460873/216872764416\) | \(45201137736063706113024\) | \([2, 2]\) | \(5529600\) | \(3.1646\) | |
| 35574.cn3 | 35574de3 | \([1, 0, 0, -8564564, 187817789424]\) | \(-333345918055753/72923718045024\) | \(-15198934879883060143127136\) | \([2]\) | \(11059200\) | \(3.5112\) | |
| 35574.cn4 | 35574de1 | \([1, 0, 0, -3821364, -951514992]\) | \(29609739866953/15259926528\) | \(3180510206949030100992\) | \([2]\) | \(2764800\) | \(2.8181\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35574.cn have rank \(1\).
Complex multiplication
The elliptic curves in class 35574.cn do not have complex multiplication.Modular form 35574.2.a.cn
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.
