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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 23400m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23400.e3 | 23400m1 | \([0, 0, 0, -8850, -320375]\) | \(420616192/117\) | \(21323250000\) | \([2]\) | \(32768\) | \(0.96371\) | \(\Gamma_0(N)\)-optimal |
| 23400.e2 | 23400m2 | \([0, 0, 0, -9975, -233750]\) | \(37642192/13689\) | \(39917124000000\) | \([2, 2]\) | \(65536\) | \(1.3103\) | |
| 23400.e4 | 23400m3 | \([0, 0, 0, 30525, -1651250]\) | \(269676572/257049\) | \(-2998219536000000\) | \([2]\) | \(131072\) | \(1.6569\) | |
| 23400.e1 | 23400m4 | \([0, 0, 0, -68475, 6727750]\) | \(3044193988/85293\) | \(994857552000000\) | \([2]\) | \(131072\) | \(1.6569\) |
Rank
sage: E.rank()
The elliptic curves in class 23400m have rank \(0\).
Complex multiplication
The elliptic curves in class 23400m do not have complex multiplication.Modular form 23400.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
