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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 18515.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18515.d1 | 18515k1 | \([1, 0, 0, -66665, 2847592]\) | \(18191447/8575\) | \(15444884072045225\) | \([2]\) | \(119232\) | \(1.8005\) | \(\Gamma_0(N)\)-optimal |
| 18515.d2 | 18515k2 | \([1, 0, 0, 237510, 21645607]\) | \(822656953/588245\) | \(-1059519047342302435\) | \([2]\) | \(238464\) | \(2.1471\) |
Rank
sage: E.rank()
The elliptic curves in class 18515.d have rank \(1\).
Complex multiplication
The elliptic curves in class 18515.d do not have complex multiplication.Modular form 18515.2.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.
