Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 31200.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31200.e1 | 31200g2 | \([0, -1, 0, -830408, -290974188]\) | \(7916055336451592/385003125\) | \(3080025000000000\) | \([2]\) | \(276480\) | \(2.0444\) | |
| 31200.e2 | 31200g1 | \([0, -1, 0, -49158, -5036688]\) | \(-13137573612736/3427734375\) | \(-3427734375000000\) | \([2]\) | \(138240\) | \(1.6979\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 31200.e have rank \(0\).
Complex multiplication
The elliptic curves in class 31200.e do not have complex multiplication.Modular form 31200.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
