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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 34496.dd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
34496.dd1 | 34496u2 | \([0, -1, 0, -735457, 243008865]\) | \(1426487591593/2156\) | \(66493151707136\) | \([2]\) | \(294912\) | \(1.9204\) | |
34496.dd2 | 34496u1 | \([0, -1, 0, -45537, 3882593]\) | \(-338608873/13552\) | \(-417956953587712\) | \([2]\) | \(147456\) | \(1.5738\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 34496.dd have rank \(0\).
Complex multiplication
The elliptic curves in class 34496.dd do not have complex multiplication.Modular form 34496.2.a.dd
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.