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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 1155.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1155.m1 | 1155l3 | \([1, 0, 1, -575018, 167782133]\) | \(21026497979043461623321/161783881875\) | \(161783881875\) | \([4]\) | \(7680\) | \(1.7433\) | |
1155.m2 | 1155l2 | \([1, 0, 1, -35963, 2615681]\) | \(5143681768032498601/14238434358225\) | \(14238434358225\) | \([2, 2]\) | \(3840\) | \(1.3967\) | |
1155.m3 | 1155l4 | \([1, 0, 1, -21788, 4702241]\) | \(-1143792273008057401/8897444448004035\) | \(-8897444448004035\) | \([2]\) | \(7680\) | \(1.7433\) | |
1155.m4 | 1155l1 | \([1, 0, 1, -3158, 4403]\) | \(3481467828171481/2005331497785\) | \(2005331497785\) | \([2]\) | \(1920\) | \(1.0501\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1155.m have rank \(0\).
Complex multiplication
The elliptic curves in class 1155.m do not have complex multiplication.Modular form 1155.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.