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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1980f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1980.c3 | 1980f1 | \([0, 0, 0, -372, -3611]\) | \(-488095744/200475\) | \(-2338340400\) | \([2]\) | \(1152\) | \(0.50603\) | \(\Gamma_0(N)\)-optimal |
| 1980.c2 | 1980f2 | \([0, 0, 0, -6447, -199226]\) | \(158792223184/16335\) | \(3048503040\) | \([2]\) | \(2304\) | \(0.85261\) | |
| 1980.c4 | 1980f3 | \([0, 0, 0, 2868, 39481]\) | \(223673040896/187171875\) | \(-2183172750000\) | \([6]\) | \(3456\) | \(1.0553\) | |
| 1980.c1 | 1980f4 | \([0, 0, 0, -14007, 346606]\) | \(1628514404944/664335375\) | \(123980925024000\) | \([6]\) | \(6912\) | \(1.4019\) |
Rank
sage: E.rank()
The elliptic curves in class 1980f have rank \(1\).
Complex multiplication
The elliptic curves in class 1980f do not have complex multiplication.Modular form 1980.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
