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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 13860.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13860.m1 | 13860p2 | \([0, 0, 0, -887575503, 10152728950502]\) | \(414354576760345737269208016/1182266314178222109375\) | \(220639268617196522940000000\) | \([2]\) | \(6988800\) | \(3.9263\) | |
13860.m2 | 13860p1 | \([0, 0, 0, -33278628, 286796059877]\) | \(-349439858058052607328256/2844147488104248046875\) | \(-33174136301247949218750000\) | \([2]\) | \(3494400\) | \(3.5798\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13860.m have rank \(1\).
Complex multiplication
The elliptic curves in class 13860.m do not have complex multiplication.Modular form 13860.2.a.m
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.