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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 7920.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7920.b1 | 7920g3 | \([0, 0, 0, -67923, -350622]\) | \(46424454082884/26794860125\) | \(20002255903872000\) | \([2]\) | \(73728\) | \(1.8174\) | |
| 7920.b2 | 7920g2 | \([0, 0, 0, -45423, 3712878]\) | \(55537159171536/228765625\) | \(42693156000000\) | \([2, 2]\) | \(36864\) | \(1.4708\) | |
| 7920.b3 | 7920g1 | \([0, 0, 0, -45378, 3720627]\) | \(885956203616256/15125\) | \(176418000\) | \([2]\) | \(18432\) | \(1.1243\) | \(\Gamma_0(N)\)-optimal |
| 7920.b4 | 7920g4 | \([0, 0, 0, -23643, 7280442]\) | \(-1957960715364/29541015625\) | \(-22052250000000000\) | \([2]\) | \(73728\) | \(1.8174\) |
Rank
sage: E.rank()
The elliptic curves in class 7920.b have rank \(0\).
Complex multiplication
The elliptic curves in class 7920.b do not have complex multiplication.Modular form 7920.2.a.b
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.
