Show commands:
SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 162240dl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.k2 | 162240dl1 | \([0, -1, 0, -1329241, -710059559]\) | \(-13137573612736/3427734375\) | \(-67768398360000000000\) | \([2]\) | \(3870720\) | \(2.5222\) | \(\Gamma_0(N)\)-optimal |
| 162240.k1 | 162240dl2 | \([0, -1, 0, -22454241, -40944734559]\) | \(7916055336451592/385003125\) | \(60893972030361600000\) | \([2]\) | \(7741440\) | \(2.8688\) |
Rank
sage: E.rank()
The elliptic curves in class 162240dl have rank \(0\).
Complex multiplication
The elliptic curves in class 162240dl do not have complex multiplication.Modular form 162240.2.a.dl
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 Cremona 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 Cremona labels.
