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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 1155.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1155.l1 | 1155h3 | \([1, 0, 1, -2054, -35989]\) | \(957681397954009/31185\) | \(31185\) | \([2]\) | \(384\) | \(0.36359\) | |
1155.l2 | 1155h4 | \([1, 0, 1, -204, 151]\) | \(932288503609/527295615\) | \(527295615\) | \([2]\) | \(384\) | \(0.36359\) | |
1155.l3 | 1155h2 | \([1, 0, 1, -129, -569]\) | \(234770924809/1334025\) | \(1334025\) | \([2, 2]\) | \(192\) | \(0.017018\) | |
1155.l4 | 1155h1 | \([1, 0, 1, -4, -19]\) | \(-4826809/144375\) | \(-144375\) | \([2]\) | \(96\) | \(-0.32956\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1155.l have rank \(1\).
Complex multiplication
The elliptic curves in class 1155.l do not have complex multiplication.Modular form 1155.2.a.l
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.