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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 59150e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59150.p2 | 59150e1 | \([1, -1, 0, -91446692, 336053179216]\) | \(510408052788213/980000000\) | \(162381396649062500000000\) | \([2]\) | \(10063872\) | \(3.3429\) | \(\Gamma_0(N)\)-optimal |
| 59150.p1 | 59150e2 | \([1, -1, 0, -122204692, 90450549216]\) | \(1218083778723573/683593750000\) | \(113268273332214355468750000\) | \([2]\) | \(20127744\) | \(3.6895\) |
Rank
sage: E.rank()
The elliptic curves in class 59150e have rank \(2\).
Complex multiplication
The elliptic curves in class 59150e do not have complex multiplication.Modular form 59150.2.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 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.
