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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 151725.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 151725.bb1 | 151725w4 | \([1, 0, 0, -160601063, -783389006508]\) | \(1214661886599131209/2213451765\) | \(834802261029051328125\) | \([2]\) | \(21233664\) | \(3.2715\) | |
| 151725.bb2 | 151725w3 | \([1, 0, 0, -26721813, 37186394742]\) | \(5595100866606889/1653777286875\) | \(623721302696532919921875\) | \([2]\) | \(21233664\) | \(3.2715\) | |
| 151725.bb3 | 151725w2 | \([1, 0, 0, -10140438, -11977382133]\) | \(305759741604409/12646127025\) | \(4769480682010972265625\) | \([2, 2]\) | \(10616832\) | \(2.9250\) | |
| 151725.bb4 | 151725w1 | \([1, 0, 0, 299687, -691607008]\) | \(7892485271/552491415\) | \(-208371869554220859375\) | \([2]\) | \(5308416\) | \(2.5784\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 151725.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 151725.bb do not have complex multiplication.Modular form 151725.2.a.bb
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.
