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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 3570.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3570.h1 | 3570i3 | \([1, 1, 0, -5640217, 5153400421]\) | \(19843180007106582309156121/1586964960000\) | \(1586964960000\) | \([4]\) | \(61440\) | \(2.2320\) | |
| 3570.h2 | 3570i2 | \([1, 1, 0, -352537, 80400229]\) | \(4845512858070228485401/1370018429337600\) | \(1370018429337600\) | \([2, 2]\) | \(30720\) | \(1.8854\) | |
| 3570.h3 | 3570i4 | \([1, 1, 0, -307737, 101644389]\) | \(-3223035316613162194201/2609328690805052160\) | \(-2609328690805052160\) | \([2]\) | \(61440\) | \(2.2320\) | |
| 3570.h4 | 3570i1 | \([1, 1, 0, -24857, 905061]\) | \(1698623579042432281/620987846492160\) | \(620987846492160\) | \([2]\) | \(15360\) | \(1.5389\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3570.h have rank \(0\).
Complex multiplication
The elliptic curves in class 3570.h do not have complex multiplication.Modular form 3570.2.a.h
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.
