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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 380880.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 380880.d1 | 380880d2 | \([0, 0, 0, -6003, 178802]\) | \(17779581/25\) | \(33639321600\) | \([2]\) | \(638976\) | \(0.92341\) | |
| 380880.d2 | 380880d1 | \([0, 0, 0, -483, 1058]\) | \(9261/5\) | \(6727864320\) | \([2]\) | \(319488\) | \(0.57684\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 380880.d have rank \(3\).
Complex multiplication
The elliptic curves in class 380880.d do not have complex multiplication.Modular form 380880.2.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.
