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SageMath
E = EllipticCurve("ec1")
E.isogeny_class()
Elliptic curves in class 303450.ec
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303450.ec1 | 303450ec2 | \([1, 1, 1, -46243763, -123841108969]\) | \(-1159924308480625/31212514998\) | \(-294294622823343696093750\) | \([]\) | \(44789760\) | \(3.2851\) | |
303450.ec2 | 303450ec1 | \([1, 1, 1, 2524987, -690261469]\) | \(188819819375/131167512\) | \(-1236744090413409375000\) | \([]\) | \(14929920\) | \(2.7358\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303450.ec have rank \(1\).
Complex multiplication
The elliptic curves in class 303450.ec do not have complex multiplication.Modular form 303450.2.a.ec
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.