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SageMath
sage: E = EllipticCurve("p1")
sage: E.isogeny_class()
Elliptic curves in class 60984.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60984.p1 | 60984ch4 | \([0, 0, 0, -325611, 71514630]\) | \(1443468546/7\) | \(18514484803584\) | \([2]\) | \(327680\) | \(1.7462\) | |
| 60984.p2 | 60984ch3 | \([0, 0, 0, -64251, -4959306]\) | \(11090466/2401\) | \(6350468287629312\) | \([2]\) | \(327680\) | \(1.7462\) | |
| 60984.p3 | 60984ch2 | \([0, 0, 0, -20691, 1078110]\) | \(740772/49\) | \(64800696812544\) | \([2, 2]\) | \(163840\) | \(1.3996\) | |
| 60984.p4 | 60984ch1 | \([0, 0, 0, 1089, 71874]\) | \(432/7\) | \(-2314310600448\) | \([2]\) | \(81920\) | \(1.0531\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 60984.p have rank \(1\).
Complex multiplication
The elliptic curves in class 60984.p do not have complex multiplication.Modular form 60984.2.a.p
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.
