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SageMath
E = EllipticCurve("mh1")
E.isogeny_class()
Elliptic curves in class 369600.mh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.mh1 | 369600mh3 | \([0, 1, 0, -14901633, -21906511137]\) | \(89343998142858649/1112702976000\) | \(4557631389696000000000\) | \([2]\) | \(23887872\) | \(2.9657\) | |
| 369600.mh2 | 369600mh4 | \([0, 1, 0, -2613633, -56939599137]\) | \(-482056280171929/341652696000000\) | \(-1399409442816000000000000\) | \([2]\) | \(47775744\) | \(3.3122\) | |
| 369600.mh3 | 369600mh1 | \([0, 1, 0, -1437633, 647272863]\) | \(80224711835689/2173469760\) | \(8902532136960000000\) | \([2]\) | \(7962624\) | \(2.4164\) | \(\Gamma_0(N)\)-optimal |
| 369600.mh4 | 369600mh2 | \([0, 1, 0, 290367, 2107432863]\) | \(661003929431/468755040600\) | \(-1920020646297600000000\) | \([2]\) | \(15925248\) | \(2.7629\) |
Rank
sage: E.rank()
The elliptic curves in class 369600.mh have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.mh do not have complex multiplication.Modular form 369600.2.a.mh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
