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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 35520bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35520.t3 | 35520bz1 | \([0, -1, 0, -1340, -18438]\) | \(4160851280704/624375\) | \(39960000\) | \([2]\) | \(18432\) | \(0.47180\) | \(\Gamma_0(N)\)-optimal |
| 35520.t2 | 35520bz2 | \([0, -1, 0, -1465, -14663]\) | \(84951891136/24950025\) | \(102195302400\) | \([2, 2]\) | \(36864\) | \(0.81838\) | |
| 35520.t4 | 35520bz3 | \([0, -1, 0, 3935, -102143]\) | \(205587930808/253011735\) | \(-8290688532480\) | \([2]\) | \(73728\) | \(1.1650\) | |
| 35520.t1 | 35520bz4 | \([0, -1, 0, -8865, 312417]\) | \(2351575819592/98316585\) | \(3221637857280\) | \([2]\) | \(73728\) | \(1.1650\) |
Rank
sage: E.rank()
The elliptic curves in class 35520bz have rank \(1\).
Complex multiplication
The elliptic curves in class 35520bz do not have complex multiplication.Modular form 35520.2.a.bz
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
