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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 133952.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 133952.bj1 | 133952ch3 | \([0, 0, 0, -178604, 29052592]\) | \(9614292367656708/2093\) | \(137166848\) | \([2]\) | \(262144\) | \(1.3858\) | |
| 133952.bj2 | 133952ch4 | \([0, 0, 0, -13004, 294128]\) | \(3710860803108/1577224103\) | \(103364958814208\) | \([2]\) | \(262144\) | \(1.3858\) | |
| 133952.bj3 | 133952ch2 | \([0, 0, 0, -11164, 453840]\) | \(9392111857872/4380649\) | \(71772553216\) | \([2, 2]\) | \(131072\) | \(1.0392\) | |
| 133952.bj4 | 133952ch1 | \([0, 0, 0, -584, 9480]\) | \(-21511084032/25465531\) | \(-26076703744\) | \([2]\) | \(65536\) | \(0.69262\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 133952.bj have rank \(2\).
Complex multiplication
The elliptic curves in class 133952.bj do not have complex multiplication.Modular form 133952.2.a.bj
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.
