Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 301665.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 301665.k1 | 301665k4 | \([1, 1, 1, -538860, -152464590]\) | \(3585019225176649/316207395\) | \(1526272700052555\) | \([2]\) | \(3538944\) | \(1.9543\) | |
| 301665.k2 | 301665k3 | \([1, 1, 1, -195790, 31567622]\) | \(171963096231529/9865918125\) | \(47620902399013125\) | \([2]\) | \(3538944\) | \(1.9543\) | |
| 301665.k3 | 301665k2 | \([1, 1, 1, -36085, -2034310]\) | \(1076575468249/258084225\) | \(1245723259988025\) | \([2, 2]\) | \(1769472\) | \(1.6077\) | |
| 301665.k4 | 301665k1 | \([1, 1, 1, 5320, -195928]\) | \(3449795831/5510295\) | \(-26597141498655\) | \([2]\) | \(884736\) | \(1.2612\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 301665.k have rank \(0\).
Complex multiplication
The elliptic curves in class 301665.k do not have complex multiplication.Modular form 301665.2.a.k
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.
