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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 151725.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 151725.w1 | 151725bd4 | \([1, 1, 1, -23037063, -42565097094]\) | \(3585019225176649/316207395\) | \(119257465861293046875\) | \([2]\) | \(10616832\) | \(2.8932\) | |
| 151725.w2 | 151725bd3 | \([1, 1, 1, -8370313, 8843378906]\) | \(171963096231529/9865918125\) | \(3720926242039658203125\) | \([2]\) | \(10616832\) | \(2.8932\) | |
| 151725.w3 | 151725bd2 | \([1, 1, 1, -1542688, -565088344]\) | \(1076575468249/258084225\) | \(97336340449203515625\) | \([2, 2]\) | \(5308416\) | \(2.5466\) | |
| 151725.w4 | 151725bd1 | \([1, 1, 1, 227437, -55292344]\) | \(3449795831/5510295\) | \(-2078205090200859375\) | \([4]\) | \(2654208\) | \(2.2000\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 151725.w have rank \(0\).
Complex multiplication
The elliptic curves in class 151725.w do not have complex multiplication.Modular form 151725.2.a.w
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.
