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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 439824.dv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
439824.dv1 | 439824dv2 | \([0, 1, 0, -142704, 20700756]\) | \(666940371553/37026\) | \(17842470395904\) | \([2]\) | \(1658880\) | \(1.6081\) | \(\Gamma_0(N)\)-optimal* |
439824.dv2 | 439824dv1 | \([0, 1, 0, -9424, 282260]\) | \(192100033/38148\) | \(18383151316992\) | \([2]\) | \(829440\) | \(1.2615\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 439824.dv have rank \(1\).
Complex multiplication
The elliptic curves in class 439824.dv do not have complex multiplication.Modular form 439824.2.a.dv
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.