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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 79475.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 79475.m1 | 79475k4 | \([1, -1, 1, -427630, 107713122]\) | \(22930509321/6875\) | \(2592902919921875\) | \([2]\) | \(442368\) | \(1.9357\) | |
| 79475.m2 | 79475k3 | \([1, -1, 1, -210880, -36353378]\) | \(2749884201/73205\) | \(27609230291328125\) | \([2]\) | \(442368\) | \(1.9357\) | |
| 79475.m3 | 79475k2 | \([1, -1, 1, -30255, 1216622]\) | \(8120601/3025\) | \(1140877284765625\) | \([2, 2]\) | \(221184\) | \(1.5891\) | |
| 79475.m4 | 79475k1 | \([1, -1, 1, 5870, 132872]\) | \(59319/55\) | \(-20743223359375\) | \([2]\) | \(110592\) | \(1.2425\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 79475.m have rank \(0\).
Complex multiplication
The elliptic curves in class 79475.m do not have complex multiplication.Modular form 79475.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
