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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1520.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1520.f1 | 1520b3 | \([0, 0, 0, -2027, -35126]\) | \(899466517764/95\) | \(97280\) | \([2]\) | \(512\) | \(0.38532\) | |
| 1520.f2 | 1520b4 | \([0, 0, 0, -227, 434]\) | \(1263284964/651605\) | \(667243520\) | \([4]\) | \(512\) | \(0.38532\) | |
| 1520.f3 | 1520b2 | \([0, 0, 0, -127, -546]\) | \(884901456/9025\) | \(2310400\) | \([2, 2]\) | \(256\) | \(0.038746\) | |
| 1520.f4 | 1520b1 | \([0, 0, 0, -2, -21]\) | \(-55296/11875\) | \(-190000\) | \([2]\) | \(128\) | \(-0.30783\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1520.f have rank \(1\).
Complex multiplication
The elliptic curves in class 1520.f do not have complex multiplication.Modular form 1520.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
