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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 59150.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59150.d1 | 59150y2 | \([1, 0, 1, -15547666, -23501553372]\) | \(313558873425953/1475789056\) | \(1956250514879032736000\) | \([2]\) | \(5111808\) | \(2.9351\) | |
| 59150.d2 | 59150y1 | \([1, 0, 1, -1486866, 64347428]\) | \(274244925473/157351936\) | \(208579813331542016000\) | \([2]\) | \(2555904\) | \(2.5886\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59150.d have rank \(1\).
Complex multiplication
The elliptic curves in class 59150.d do not have complex multiplication.Modular form 59150.2.a.d
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.
