Show commands:
SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 107712.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107712.ch1 | 107712ds3 | \([0, 0, 0, -9558471180, -359691989621744]\) | \(505384091400037554067434625/815656731648\) | \(155874428812366184448\) | \([2]\) | \(53084160\) | \(4.0300\) | |
| 107712.ch2 | 107712ds4 | \([0, 0, 0, -9558379020, -359699272510448]\) | \(-505369473241574671219626625/20303219722982711328\) | \(-3880005711443891731329712128\) | \([2]\) | \(106168320\) | \(4.3765\) | |
| 107712.ch3 | 107712ds1 | \([0, 0, 0, -118338060, -490486569968]\) | \(959024269496848362625/11151660319506432\) | \(2131115474398790006341632\) | \([2]\) | \(17694720\) | \(3.4807\) | \(\Gamma_0(N)\)-optimal |
| 107712.ch4 | 107712ds2 | \([0, 0, 0, -23966220, -1251236846576]\) | \(-7966267523043306625/3534510366354604032\) | \(-675455449713215101816799232\) | \([2]\) | \(35389440\) | \(3.8272\) |
Rank
sage: E.rank()
The elliptic curves in class 107712.ch have rank \(0\).
Complex multiplication
The elliptic curves in class 107712.ch do not have complex multiplication.Modular form 107712.2.a.ch
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
