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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 334620.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 334620.d1 | 334620d1 | \([0, 0, 0, -938028, 349680773]\) | \(3561997012123648/601425\) | \(15412001576400\) | \([2]\) | \(3741696\) | \(1.9299\) | \(\Gamma_0(N)\)-optimal |
| 334620.d2 | 334620d2 | \([0, 0, 0, -935103, 351969878]\) | \(-220548705213328/2893696245\) | \(-1186452870155055360\) | \([2]\) | \(7483392\) | \(2.2765\) |
Rank
sage: E.rank()
The elliptic curves in class 334620.d have rank \(1\).
Complex multiplication
The elliptic curves in class 334620.d do not have complex multiplication.Modular form 334620.2.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.
