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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 39326.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39326.m1 | 39326l6 | \([1, 1, 1, -7670033, -8179253777]\) | \(2251439055699625/25088\) | \(556059492004352\) | \([2]\) | \(898560\) | \(2.3982\) | |
39326.m2 | 39326l5 | \([1, 1, 1, -478993, -128165393]\) | \(-548347731625/1835008\) | \(-40671779986604032\) | \([2]\) | \(449280\) | \(2.0517\) | |
39326.m3 | 39326l4 | \([1, 1, 1, -99778, -9985145]\) | \(4956477625/941192\) | \(20860919379725768\) | \([2]\) | \(299520\) | \(1.8489\) | |
39326.m4 | 39326l2 | \([1, 1, 1, -29553, 1941869]\) | \(128787625/98\) | \(2172107390642\) | \([2]\) | \(99840\) | \(1.2996\) | |
39326.m5 | 39326l1 | \([1, 1, 1, -1463, 42985]\) | \(-15625/28\) | \(-620602111612\) | \([2]\) | \(49920\) | \(0.95306\) | \(\Gamma_0(N)\)-optimal |
39326.m6 | 39326l3 | \([1, 1, 1, 12582, -906457]\) | \(9938375/21952\) | \(-486552055503808\) | \([2]\) | \(149760\) | \(1.5024\) |
Rank
sage: E.rank()
The elliptic curves in class 39326.m have rank \(1\).
Complex multiplication
The elliptic curves in class 39326.m do not have complex multiplication.Modular form 39326.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.