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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 33930.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33930.r1 | 33930ba4 | \([1, -1, 1, -75173, 7281897]\) | \(64443098670429961/6032611833300\) | \(4397774026475700\) | \([2]\) | \(393216\) | \(1.7400\) | |
| 33930.r2 | 33930ba2 | \([1, -1, 1, -16673, -697503]\) | \(703093388853961/115124490000\) | \(83925753210000\) | \([2, 2]\) | \(196608\) | \(1.3935\) | |
| 33930.r3 | 33930ba1 | \([1, -1, 1, -15953, -771519]\) | \(615882348586441/21715200\) | \(15830380800\) | \([2]\) | \(98304\) | \(1.0469\) | \(\Gamma_0(N)\)-optimal |
| 33930.r4 | 33930ba3 | \([1, -1, 1, 30307, -3948519]\) | \(4223169036960119/11647532812500\) | \(-8491051420312500\) | \([2]\) | \(393216\) | \(1.7400\) |
Rank
sage: E.rank()
The elliptic curves in class 33930.r have rank \(0\).
Complex multiplication
The elliptic curves in class 33930.r do not have complex multiplication.Modular form 33930.2.a.r
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.
